diff --git a/Lib/posixpath.py b/Lib/posixpath.py
index 259baa64b1..feff7857be 100644
--- a/Lib/posixpath.py
+++ b/Lib/posixpath.py
@@ -336,6 +336,7 @@ def expandvars(path):
 
 def normpath(path):
     """Normalize path, eliminating double slashes, etc."""
+    normalize_dotdot = True
     path = os.fspath(path)
     if isinstance(path, bytes):
         sep = b'/'
@@ -360,11 +361,20 @@ def normpath(path):
     for comp in comps:
         if comp in (empty, dot):
             continue
-        if (comp != dotdot or (not initial_slashes and not new_comps) or
-             (new_comps and new_comps[-1] == dotdot)):
+        try:
+            os.lstat(sep.join(new_comps))
+        except OSError:
+            normalize_dotdot = False
+
+        comp_dotdot = comp == dotdot
+        if ((comp_dotdot and not normalize_dotdot) or not comp_dotdot or
+                (not initial_slashes and not new_comps) or
+                (new_comps and new_comps[-1] == dotdot)):
             new_comps.append(comp)
+
         elif new_comps:
             new_comps.pop()
+
     comps = new_comps
     path = sep.join(comps)
     if initial_slashes:
@@ -430,7 +440,8 @@ def _joinrealpath(path, rest, strict, seen):
         except OSError:
             if strict:
                 raise
-            is_link = False
+            # Return already resolved part + rest of the path unchanged.
+            return join(newpath, rest), False
         else:
             is_link = stat.S_ISLNK(st.st_mode)
         if not is_link: