diff --git a/swh/web/api/views/origin.py b/swh/web/api/views/origin.py
--- a/swh/web/api/views/origin.py
+++ b/swh/web/api/views/origin.py
@@ -222,9 +222,14 @@
         pattern or match a provided regular expression.
         The search is performed in a case insensitive way.
 
+        .. warning::
+
+            This endpoint used to provide an `offset` query parameter,
+            and guarantee an order on results. This is no longer true,
+            and only the Link header should be used for paginating through
+            results.
+
         :param string url_pattern: a string pattern or a regular expression
-        :query int offset: the number of found origins to skip before returning
-            results
         :query int limit: the maximum number of found origins to return
         :query boolean regexp: if true, consider provided pattern as a regular
             expression and search origins whose urls match it
@@ -234,6 +239,7 @@
         {return_origin_array}
 
         {common_headers}
+        {resheader_link}
 
         **Allowed HTTP Methods:** :http:method:`get`, :http:method:`head`,
         :http:method:`options`