diff --git a/Lib/glob.py b/Lib/glob.py
--- a/Lib/glob.py
+++ b/Lib/glob.py
@@ -53,13 +53,23 @@
         else:
             yield from glob1(dirname, basename)
         return
-    # `os.path.split()` returns the argument itself as a dirname if it is a
-    # drive or UNC path.  Prevent an infinite recursion if a drive or UNC path
-    # contains magic characters (i.e. r'\\?\C:').
-    if dirname != pathname and has_magic(dirname):
-        dirs = _iglob(dirname, recursive)
+
+    if has_magic(dirname):
+        # `os.path.split()` returns the argument itself as a dirname if it is
+        # a drive or UNC path.  Prevent an infinite recursion if a drive or
+        # UNC path contains magic characters (i.e. r'\\?\C:').
+      if dirname == pathname:
+        # Here, dirname may not be an existing directory, this will be checked
+        # for by glob0().
+        dirs = [dirname]
+      else:
+        dirs = (d for d in _iglob(dirname, recursive) if
+                                                not d or os.path.isdir(d))
+    elif os.path.isdir(dirname):
+        dirs = [dirname]
     else:
-        dirs = [dirname]
+        return
+
     if has_magic(basename):
         if recursive and _isrecursive(basename):
             glob_in_dir = glob2
@@ -76,13 +86,8 @@
 # takes a literal basename (so it only has to check for its existence).
 
 def glob1(dirname, pattern):
-    if not dirname:
-        if isinstance(pattern, bytes):
-            dirname = bytes(os.curdir, 'ASCII')
-        else:
-            dirname = os.curdir
     try:
-        names = os.listdir(dirname)
+        names = _listdir(dirname)
     except OSError:
         return []
     if not _ishidden(pattern):
@@ -110,21 +115,17 @@
 
 # Recursively yields relative pathnames inside a literal directory.
 def _rlistdir(dirname):
-    if not dirname:
-        if isinstance(dirname, bytes):
-            dirname = bytes(os.curdir, 'ASCII')
-        else:
-            dirname = os.curdir
     try:
-        names = os.listdir(dirname)
+        names = _listdir(dirname)
     except os.error:
         return
     for x in names:
         if not _ishidden(x):
             yield x
             path = os.path.join(dirname, x) if dirname else x
-            for y in _rlistdir(path):
-                yield os.path.join(x, y)
+            if os.path.isdir(path):
+                for y in _rlistdir(path):
+                    yield os.path.join(x, y)
 
 
 magic_check = re.compile('([*?[])')
@@ -146,6 +147,16 @@
     else:
         return pattern == '**'
 
+def _listdir(dirname):
+    if not dirname:
+        if isinstance(dirname, bytes):
+            dirname = bytes(os.curdir, 'ASCII')
+        else:
+            dirname = os.curdir
+    else:
+        assert os.path.isdir(dirname)
+    return os.listdir(dirname)
+
 def escape(pathname):
     """Escape all special characters.
     """