diff --git a/wp-admin/includes/update-core.php b/wp-admin/includes/update-core.php
index 9f17a086d9..4a077dc62c 100644
--- a/wp-admin/includes/update-core.php
+++ b/wp-admin/includes/update-core.php
@@ -1076,7 +1076,11 @@ function update_core($from, $to) {
 		$old_file = $to . $old_file;
 		if ( !$wp_filesystem->exists($old_file) )
 			continue;
-		$wp_filesystem->delete($old_file, true);
+
+		// If the file isn't deleted, try writing an empty string to the file instead.
+		if ( ! $wp_filesystem->delete( $old_file, true ) && $wp_filesystem->is_file( $old_file ) ) {
+			$wp_filesystem->put_contents( $old_file, '' );
+		}
 	}
 
 	// Remove any Genericons example.html's from the filesystem