Can we handle browser close event instead of 'beforeunload'?

Question

how to handle browser close event? I tried using 'beforeunload' event which is also firing on page refresh, any solution?

window.onbeforeunload = function (event) {

        var message = 'Important: Please click on \'Save\' button to leave this page.';
        if (typeof event == 'undefined') {
            event = window.event;
        }
        if (event) {
            event.returnValue = message;
        }
        return message;
    };