Index: tests/regressiontests/defaultfilters/tests.py
===================================================================
--- tests/regressiontests/defaultfilters/tests.py	(revision 7569)
+++ tests/regressiontests/defaultfilters/tests.py	(working copy)
@@ -166,6 +166,11 @@
 >>> urlizetrunc(uri, 2)
 u'<a href="http://31characteruri.com/test/" rel="nofollow">...</a>'
 
+# Check normal urlize
+>>> url = 'https://google.com'
+>>> urlize(url)
+u'<a href="https://google.com" rel="nofollow">https://google.com</a>'
+
 >>> wordcount('')
 0
 
Index: django/utils/html.py
===================================================================
--- django/utils/html.py	(revision 7079)
+++ django/utils/html.py	(working copy)
@@ -99,7 +99,7 @@
          lead, middle, trail = match.groups()
          if safe_input:
              middle = mark_safe(middle)
-            if middle.startswith('www.') or ('@' not in middle and not middle.startswith('http://') and \
+            if middle.startswith('www.') or ('@' not in middle and not (middle.startswith('http://') or middle.startswith('https://')) and \
                  len(middle) > 0 and middle[0] in string.ascii_letters + string.digits and \
                  (middle.endswith('.org') or middle.endswith('.net') or middle.endswith('.com'))):
              middle = 'http://%s' % middle