Index: src/js/_enqueues/vendor/plupload/handlers.js
===================================================================
--- src/js/_enqueues/vendor/plupload/handlers.js	(revision 60899)
+++ src/js/_enqueues/vendor/plupload/handlers.js	(working copy)
@@ -420,11 +420,11 @@
 			target.parents( '.media-item' ).fadeOut( 200, function() {
 				$( this ).remove();
 			} );
-		} else if ( target.is( '.upload-flash-bypass a' ) || target.is( 'a.uploader-html' ) ) { // Switch uploader to html4.
+		} else if ( target.is( '.upload-flash-bypass button' ) || target.is( 'a.uploader-html' ) ) { // Switch uploader to html4.
 			$( '#media-items, p.submit, span.big-file-warning' ).css( 'display', 'none' );
 			switchUploader( 0 );
 			e.preventDefault();
-		} else if ( target.is( '.upload-html-bypass a' ) ) { // Switch uploader to multi-file.
+		} else if ( target.is( '.upload-html-bypass button' ) ) { // Switch uploader to multi-file.
 			$( '#media-items, p.submit, span.big-file-warning' ).css( 'display', '' );
 			switchUploader( 1 );
 			e.preventDefault();
Index: src/wp-admin/includes/media.php
===================================================================
--- src/wp-admin/includes/media.php	(revision 60899)
+++ src/wp-admin/includes/media.php	(working copy)
@@ -3045,10 +3045,9 @@
 	<p class="upload-flash-bypass">
 	<?php
 		printf(
-			/* translators: 1: URL to browser uploader, 2: Additional link attributes. */
-			__( 'You are using the multi-file uploader. Problems? Try the <a href="%1$s" %2$s>browser uploader</a> instead.' ),
-			$browser_uploader,
-			'target="_blank"'
+			/* translators: %s: HTML attributes for button. */
+			__( 'You are using the multi-file uploader. Problems? Try the <button %s>browser uploader</button> instead.' ),
+			'type="button" class="button-link"'
 		);
 	?>
 	</p>
@@ -3063,7 +3062,13 @@
 function media_upload_html_bypass() {
 	?>
 	<p class="upload-html-bypass hide-if-no-js">
-		<?php _e( 'You are using the browser&#8217;s built-in file uploader. The WordPress uploader includes multiple file selection and drag and drop capability. <a href="#">Switch to the multi-file uploader</a>.' ); ?>
+	<?php
+		printf(
+			/* translators: %s: HTML attributes for button. */
+			__( 'You are using the browser&#8217;s built-in file uploader. The WordPress uploader includes multiple file selection and drag and drop capability. <button %s>Switch to the multi-file uploader</button>.' ),
+			'type="button" class="button-link"'
+		);
+	?>
 	</p>
 	<?php
 }