Do not clear the favicon for an in-page navigation.

content/browser/frame_host/navigation_controller_impl.cc

 // Copyright 2013 The Chromium Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
 /*
  * Copyright (C) 2006, 2007, 2008, 2009 Apple Inc. All rights reserved.
  * Copyright (C) 2008 Nokia Corporation and/or its subsidiary(-ies)
  * Copyright (C) 2008, 2009 Torch Mobile Inc. All rights reserved.
  *     (http://www.torchmobile.com/)
  *
@@ skipping 1194 matching lines @@
   // Update the existing FrameNavigationEntry to ensure all of its members
   // reflect the parameters coming from the renderer process.
   entry->AddOrUpdateFrameEntry(
       rfh->frame_tree_node(), params.item_sequence_number,
       params.document_sequence_number, rfh->GetSiteInstance(), nullptr,
       params.url, params.referrer, params.page_state, params.method,
       params.post_id);
 
   // The redirected to page should not inherit the favicon from the previous
   // page.
-  if (ui::PageTransitionIsRedirect(params.transition))
+  if (ui::PageTransitionIsRedirect(params.transition) && !is_in_page)
     entry->GetFavicon() = FaviconStatus();
 
   // The entry we found in the list might be pending if the user hit
   // back/forward/reload. This load should commit it (since it's already in the
   // list, we can just discard the pending pointer).  We should also discard the
   // pending entry if it corresponds to a different navigation, since that one
   // is now likely canceled.  If it is not canceled, we will treat it as a new
   // navigation when it arrives, which is also ok.
   //
   // Note that we need to use the "internal" version since we don't want to
@@ skipping 875 matching lines @@
     }
   }
 }
 
 void NavigationControllerImpl::SetGetTimestampCallbackForTest(
     const base::Callback<base::Time()>& get_timestamp_callback) {
   get_timestamp_callback_ = get_timestamp_callback;
 }
 
 }  // namespace content