diff --git a/zerver/lib/bugdown/__init__.py b/zerver/lib/bugdown/__init__.py
index 51a6c5cb52..4679b878b8 100644
--- a/zerver/lib/bugdown/__init__.py
+++ b/zerver/lib/bugdown/__init__.py
@@ -982,15 +982,26 @@ def url_to_a(url, text = None):
     a = markdown.util.etree.Element('a')
 
     href = sanitize_url(url)
+    target_blank = True
     if href is None:
         # Rejected by sanitize_url; render it as plain text.
         return url
     if text is None:
         text = markdown.util.AtomicString(url)
 
+    target_blank = 'mailto:' not in href[:7]
+
+    if db_data:
+        # If the link points to a local destination we can just switch to that
+        # instead of opening a new tab.
+        local_link = re.match("^{}\/(#.+)$".format(re.escape(db_data['realm_uri'])), url)
+        if local_link:
+            href = local_link.group(1)
+            target_blank = False
+
     a.set('href', href)
     a.text = text
-    fixup_link(a, 'mailto:' not in href[:7])
+    fixup_link(a, target_blank)
     return a
 
 class VerbosePattern(markdown.inlinepatterns.Pattern):
@@ -1719,6 +1730,7 @@ def do_convert(content, message=None, message_realm=None, possible_words=None, s
             'email_info': email_info,
             'mention_data': mention_data,
             'realm_emoji': realm_emoji,
+            'realm_uri': message_realm.uri,
             'sent_by_bot': sent_by_bot,
             'stream_names': stream_name_info,
         }
diff --git a/zerver/tests/test_bugdown.py b/zerver/tests/test_bugdown.py
index 1ae7a57d31..d9ee19708a 100644
--- a/zerver/tests/test_bugdown.py
+++ b/zerver/tests/test_bugdown.py
@@ -1168,6 +1168,30 @@ class BugdownTest(ZulipTestCase):
                           '<p>I am writing this message to test something. I am writing this message to test something.</p>'
         self.assertEqual(converted, expected_output)
 
+    def test_normal_link(self):
+        # type: () -> None
+        realm = get_realm("zulip")
+        sender_user_profile = self.example_user('othello')
+        message = Message(sender=sender_user_profile, sending_client=get_client("test"))
+        msg = "http://example.com/#settings/"
+
+        self.assertEqual(
+            bugdown.convert(msg, message_realm=realm, message=message),
+            '<p><a href="http://example.com/#settings/" target="_blank" title="http://example.com/#settings/">http://example.com/#settings/</a></p>'
+        )
+
+    def test_relative_link(self):
+        # type: () -> None
+        realm = get_realm("zulip")
+        sender_user_profile = self.example_user('othello')
+        message = Message(sender=sender_user_profile, sending_client=get_client("test"))
+        msg = "http://zulip.testserver/#narrow/stream/hello"
+
+        self.assertEqual(
+            bugdown.convert(msg, message_realm=realm, message=message),
+            '<p><a href="#narrow/stream/hello" title="#narrow/stream/hello">http://zulip.testserver/#narrow/stream/hello</a></p>'
+        )
+
 class BugdownApiTests(ZulipTestCase):
     def test_render_message_api(self):
         # type: () -> None