diff --git a/mercurial/bookmarks.py b/mercurial/bookmarks.py
--- a/mercurial/bookmarks.py
+++ b/mercurial/bookmarks.py
@@ -487,6 +487,8 @@
 
 
 def pushbookmark(repo, key, old, new):
+    if isdivergent(key):
+        return False
     if bookmarksinstore(repo):
         wlock = util.nullcontextmanager()
     else:
diff --git a/mercurial/bundle2.py b/mercurial/bundle2.py
--- a/mercurial/bundle2.py
+++ b/mercurial/bundle2.py
@@ -2368,6 +2368,11 @@
                     b'prepushkey', throw=True, **pycompat.strkwargs(hookargs)
                 )
 
+        for book, node in changes:
+            if bookmarks.isdivergent(book):
+                msg = _(b'cannot accept divergent bookmark %s!') % book
+                raise error.Abort(msg)
+
         bookstore.applychanges(op.repo, op.gettransaction(), changes)
 
         if pushkeycompat:
diff --git a/mercurial/exchange.py b/mercurial/exchange.py
--- a/mercurial/exchange.py
+++ b/mercurial/exchange.py
@@ -856,7 +856,11 @@
     for b, scid, dcid in addsrc:
         if b in explicit:
             explicit.remove(b)
-            pushop.outbookmarks.append((b, b'', scid))
+            if bookmod.isdivergent(b):
+                pushop.ui.warn(_(b'cannot push divergent bookmark %s!\n') % b)
+                pushop.bkresult = 2
+            else:
+                pushop.outbookmarks.append((b, b'', scid))
     # search for overwritten bookmark
     for b, scid, dcid in list(advdst) + list(diverge) + list(differ):
         if b in explicit:
diff --git a/relnotes/next b/relnotes/next
--- a/relnotes/next
+++ b/relnotes/next
@@ -24,6 +24,7 @@
  * Use `hg copy --forget --at-rev REV` to unmark already committed
    copies.
 
+ * prevent pushes of divergent bookmarks (foo@remote)
 
 == Bug Fixes  ==
 
diff --git a/tests/test-bookmarks-pushpull.t b/tests/test-bookmarks-pushpull.t
--- a/tests/test-bookmarks-pushpull.t
+++ b/tests/test-bookmarks-pushpull.t
@@ -328,6 +328,17 @@
 
 #endif
 
+Divergent bookmark cannot be exported
+
+  $ hg book W@default
+  $ hg push -B W@default ../a
+  pushing to ../a
+  searching for changes
+  cannot push divergent bookmark W@default!
+  no changes found
+  [2]
+  $ hg book -d W@default
+
 export the active bookmark
 
   $ hg bookmark V