diff --git a/spec/service_worker/index.html b/spec/service_worker/index.html
index 69f94bd8..461960d5 100644
--- a/spec/service_worker/index.html
+++ b/spec/service_worker/index.html
@@ -886,14 +886,7 @@ <h1>_Update</h1>
               <li>Abort these steps.</li>
             </ol>
           </li>
-          <li>If fetching the script fails due to the server returning a 4xx response, then:
-            <ol>
-              <li>Reject <var>promise</var> with the result of running the <a href="#internal-unregistration-algorithm">_Unregistration algorithm</a> passing <var>serviceWorkerRegistration</var>.<var>scope</var> as the argument.</li>
-              <li>Set <var>serviceWorkerRegistration</var>.<var>updatePromise</var> to null.</li>
-              <li>Abort these steps.</li>
-            </ol>
-          </li>
-          <li>Else if fetching the script fails due to the server returning a 5xx response, or there is a DNS error, or the connection times out, then:
+          <li>Else if fetching the script fails due to the server returning a 4xx response or if fetching the script fails due to the server returning a 5xx response, or there is a DNS error, or the connection times out, then:
             <ol>
               <li>Reject <var>promise</var> with a new <code>NetworkError</code>.</li>
               <li>Set <var>serviceWorkerRegistration</var>.<var>updatePromise</var> to null.</li>