diff --git a/Lib/base64.py b/Lib/base64.py
--- a/Lib/base64.py
+++ b/Lib/base64.py
@@ -28,6 +28,7 @@
 
 
 bytes_types = (bytes, bytearray)  # Types acceptable as binary data
+ascii_types = bytes_types + (str,)
 
 
 def _translate(s, altchars):
@@ -79,10 +80,10 @@
     discarded prior to the padding check.  If validate is True,
     non-base64-alphabet characters in the input result in a binascii.Error.
     """
-    if not isinstance(s, bytes_types):
+    if not isinstance(s, ascii_types):
         raise TypeError("expected bytes, not %s" % s.__class__.__name__)
     if altchars is not None:
-        if not isinstance(altchars, bytes_types):
+        if not isinstance(altchars, ascii_types):
             raise TypeError("expected bytes, not %s"
                             % altchars.__class__.__name__)
         assert len(altchars) == 2, repr(altchars)
@@ -211,7 +212,7 @@
     the input is incorrectly padded or if there are non-alphabet
     characters present in the input.
     """
-    if not isinstance(s, bytes_types):
+    if not isinstance(s, ascii_types):
         raise TypeError("expected bytes, not %s" % s.__class__.__name__)
     quanta, leftover = divmod(len(s), 8)
     if leftover:
@@ -220,7 +221,7 @@
     # False, or the character to map the digit 1 (one) to.  It should be
     # either L (el) or I (eye).
     if map01 is not None:
-        if not isinstance(map01, bytes_types):
+        if not isinstance(map01, ascii_types):
             raise TypeError("expected bytes, not %s" % map01.__class__.__name__)
         assert len(map01) == 1, repr(map01)
         s = _translate(s, {b'0': b'O', b'1': map01})
@@ -292,7 +293,7 @@
     s were incorrectly padded or if there are non-alphabet characters
     present in the string.
     """
-    if not isinstance(s, bytes_types):
+    if not isinstance(s, ascii_types):
         raise TypeError("expected bytes, not %s" % s.__class__.__name__)
     if casefold:
         s = s.upper()
diff --git a/Lib/test/test_base64.py b/Lib/test/test_base64.py
--- a/Lib/test/test_base64.py
+++ b/Lib/test/test_base64.py
@@ -116,9 +116,6 @@
         eq(base64.b64decode(b''), b'')
         # Test with arbitrary alternative characters
         eq(base64.b64decode(b'01a*b$cd', altchars=b'*$'), b'\xd3V\xbeo\xf7\x1d')
-        # Check if passing a str object raises an error
-        self.assertRaises(TypeError, base64.b64decode, "")
-        self.assertRaises(TypeError, base64.b64decode, b"", altchars="")
         # Test standard alphabet
         eq(base64.standard_b64decode(b"d3d3LnB5dGhvbi5vcmc="), b"www.python.org")
         eq(base64.standard_b64decode(b"YQ=="), b"a")
@@ -131,9 +128,6 @@
            b"abcdefghijklmnopqrstuvwxyz"
            b"ABCDEFGHIJKLMNOPQRSTUVWXYZ"
            b"0123456789!@#0^&*();:<>,. []{}")
-        # Check if passing a str object raises an error
-        self.assertRaises(TypeError, base64.standard_b64decode, "")
-        self.assertRaises(TypeError, base64.standard_b64decode, b"", altchars="")
         # Test with 'URL safe' alternative characters
         eq(base64.urlsafe_b64decode(b'01a-b_cd'), b'\xd3V\xbeo\xf7\x1d')
         self.assertRaises(TypeError, base64.urlsafe_b64decode, "")
@@ -157,6 +151,15 @@
             with self.assertRaises(binascii.Error):
                 base64.b64decode(bstr, validate=True)
 
+    def test_b64decode_ascii_chars(self):
+        # issue 13641: Decoding functions in the base64
+        # module could accept unicode strings.
+        tests = (('MDA=', b'00'),
+                 ('AA==', b'\x00'),
+                 ('/w==', b'\xff'))
+        for str, result in tests:
+            self.assertEqual(base64.b64decode(str), result)
+
     def test_b32encode(self):
         eq = self.assertEqual
         eq(base64.b32encode(b''), b'')
@@ -199,7 +202,6 @@
         eq(base64.b32decode(b'MLO23456'), b'b\xdd\xad\xf3\xbe')
         eq(base64.b32decode(b'M1023456', map01=b'L'), b'b\xdd\xad\xf3\xbe')
         eq(base64.b32decode(b'M1023456', map01=b'I'), b'b\x1d\xad\xf3\xbe')
-        self.assertRaises(TypeError, base64.b32decode, b"", map01="")
 
     def test_b32decode_error(self):
         self.assertRaises(binascii.Error, base64.b32decode, b'abc')