diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index 40a1d6d51..699df31de 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -46,7 +46,9 @@ Changelog
   :class:`~cryptography.hazmat.primitives.kdf.kbkdf.KBKDFCMAC` now support
   :attr:`~cryptography.hazmat.primitives.kdf.kbkdf.CounterLocation.MiddleFixed`
   counter location.
-
+* Fixed :rfc:`4514` name parsing to reverse the order of the RDNs according 
+  to the section 2.1 of the RFC, affecting method :meth:`~cryptography.x509.Name.from_rfc4514_string`
+  
 .. _v37-0-4:
 
 37.0.4 - 2022-07-05
diff --git a/src/cryptography/x509/name.py b/src/cryptography/x509/name.py
index 076606c72..702fb4b21 100644
--- a/src/cryptography/x509/name.py
+++ b/src/cryptography/x509/name.py
@@ -414,13 +414,21 @@ class _RFC4514NameParser:
         return val
 
     def parse(self) -> Name:
+        """
+        Parses the `data` string and converts it to a Name.
+
+        According to RFC4514 section 2.1 the RDNSequence must be
+        reversed when converting to string representation. So, when
+        we parse it, we need to reverse again to get the RDNs on the
+        correct order.
+        """
         rdns = [self._parse_rdn()]
 
         while self._has_data():
             self._read_char(",")
             rdns.append(self._parse_rdn())
 
-        return Name(rdns)
+        return Name(reversed(rdns))
 
     def _parse_rdn(self) -> RelativeDistinguishedName:
         nas = [self._parse_na()]
diff --git a/tests/x509/test_name.py b/tests/x509/test_name.py
index f13f875f2..de47a7a1a 100644
--- a/tests/x509/test_name.py
+++ b/tests/x509/test_name.py
@@ -59,14 +59,7 @@ class TestRFC4514:
                 Name(
                     [
                         RelativeDistinguishedName(
-                            [
-                                NameAttribute(
-                                    NameOID.ORGANIZATIONAL_UNIT_NAME, "Sales"
-                                ),
-                                NameAttribute(
-                                    NameOID.COMMON_NAME, "J.  Smith"
-                                ),
-                            ]
+                            [NameAttribute(NameOID.DOMAIN_COMPONENT, "net")]
                         ),
                         RelativeDistinguishedName(
                             [
@@ -76,7 +69,14 @@ class TestRFC4514:
                             ]
                         ),
                         RelativeDistinguishedName(
-                            [NameAttribute(NameOID.DOMAIN_COMPONENT, "net")]
+                            [
+                                NameAttribute(
+                                    NameOID.ORGANIZATIONAL_UNIT_NAME, "Sales"
+                                ),
+                                NameAttribute(
+                                    NameOID.COMMON_NAME, "J.  Smith"
+                                ),
+                            ]
                         ),
                     ]
                 ),
@@ -85,11 +85,11 @@ class TestRFC4514:
                 "CN=cryptography.io,O=PyCA,L=,ST=,C=US",
                 Name(
                     [
-                        NameAttribute(NameOID.COMMON_NAME, "cryptography.io"),
-                        NameAttribute(NameOID.ORGANIZATION_NAME, "PyCA"),
-                        NameAttribute(NameOID.LOCALITY_NAME, ""),
-                        NameAttribute(NameOID.STATE_OR_PROVINCE_NAME, ""),
                         NameAttribute(NameOID.COUNTRY_NAME, "US"),
+                        NameAttribute(NameOID.STATE_OR_PROVINCE_NAME, ""),
+                        NameAttribute(NameOID.LOCALITY_NAME, ""),
+                        NameAttribute(NameOID.ORGANIZATION_NAME, "PyCA"),
+                        NameAttribute(NameOID.COMMON_NAME, "cryptography.io"),
                     ]
                 ),
             ),
@@ -97,9 +97,9 @@ class TestRFC4514:
                 r"C=US,CN=Joe \, Smith,DC=example",
                 Name(
                     [
-                        NameAttribute(NameOID.COUNTRY_NAME, "US"),
-                        NameAttribute(NameOID.COMMON_NAME, "Joe , Smith"),
                         NameAttribute(NameOID.DOMAIN_COMPONENT, "example"),
+                        NameAttribute(NameOID.COMMON_NAME, "Joe , Smith"),
+                        NameAttribute(NameOID.COUNTRY_NAME, "US"),
                     ]
                 ),
             ),
@@ -107,9 +107,9 @@ class TestRFC4514:
                 r"C=US,CN=Jane \"J\,S\" Smith,DC=example",
                 Name(
                     [
-                        NameAttribute(NameOID.COUNTRY_NAME, "US"),
-                        NameAttribute(NameOID.COMMON_NAME, 'Jane "J,S" Smith'),
                         NameAttribute(NameOID.DOMAIN_COMPONENT, "example"),
+                        NameAttribute(NameOID.COMMON_NAME, 'Jane "J,S" Smith'),
+                        NameAttribute(NameOID.COUNTRY_NAME, "US"),
                     ]
                 ),
             ),
@@ -117,9 +117,9 @@ class TestRFC4514:
                 'C=US,CN=\\"Jane J\\,S Smith\\",DC=example',
                 Name(
                     [
-                        NameAttribute(NameOID.COUNTRY_NAME, "US"),
-                        NameAttribute(NameOID.COMMON_NAME, '"Jane J,S Smith"'),
                         NameAttribute(NameOID.DOMAIN_COMPONENT, "example"),
+                        NameAttribute(NameOID.COMMON_NAME, '"Jane J,S Smith"'),
+                        NameAttribute(NameOID.COUNTRY_NAME, "US"),
                     ]
                 ),
             ),
@@ -127,11 +127,11 @@ class TestRFC4514:
                 'C=US,CN=\\"Jane \\"J\\,S\\" Smith\\",DC=example',
                 Name(
                     [
-                        NameAttribute(NameOID.COUNTRY_NAME, "US"),
+                        NameAttribute(NameOID.DOMAIN_COMPONENT, "example"),
                         NameAttribute(
                             NameOID.COMMON_NAME, '"Jane "J,S" Smith"'
                         ),
-                        NameAttribute(NameOID.DOMAIN_COMPONENT, "example"),
+                        NameAttribute(NameOID.COUNTRY_NAME, "US"),
                     ]
                 ),
             ),
@@ -139,9 +139,9 @@ class TestRFC4514:
                 r"C=US,CN=Jane=Smith,DC=example",
                 Name(
                     [
-                        NameAttribute(NameOID.COUNTRY_NAME, "US"),
-                        NameAttribute(NameOID.COMMON_NAME, "Jane=Smith"),
                         NameAttribute(NameOID.DOMAIN_COMPONENT, "example"),
+                        NameAttribute(NameOID.COMMON_NAME, "Jane=Smith"),
+                        NameAttribute(NameOID.COUNTRY_NAME, "US"),
                     ]
                 ),
             ),
@@ -170,8 +170,8 @@ class TestRFC4514:
             "CN=Santa Claus,E=santa@north.pole", {"E": NameOID.EMAIL_ADDRESS}
         ) == Name(
             [
-                NameAttribute(NameOID.COMMON_NAME, "Santa Claus"),
                 NameAttribute(NameOID.EMAIL_ADDRESS, "santa@north.pole"),
+                NameAttribute(NameOID.COMMON_NAME, "Santa Claus"),
             ]
         )
 
@@ -182,3 +182,24 @@ class TestRFC4514:
                 NameAttribute(NameOID.EMAIL_ADDRESS, "Santa Claus"),
             ]
         )
+
+    def test_generate_parse(self):
+        name_value = Name(
+            [
+                NameAttribute(NameOID.COMMON_NAME, "Common Name 1"),
+                NameAttribute(NameOID.LOCALITY_NAME, "City for Name 1"),
+                NameAttribute(
+                    NameOID.ORGANIZATION_NAME, "Name 1 Organization"
+                ),
+            ]
+        )
+
+        assert (
+            Name.from_rfc4514_string(name_value.rfc4514_string()) == name_value
+        )
+
+        name_string = "O=Organization,L=City,CN=Common Name"
+        assert (
+            Name.from_rfc4514_string(name_string).rfc4514_string()
+            == name_string
+        )