Edit in JSFiddle

function retornar_navegador () {

    var isIE = /*@cc_on!@*/false || testCSS('msTransform');  // At least IE6
    if ( isIE ) return "IE";
    var isFirefox = testCSS('MozBoxSizing');                 // FF 0.8+
    if ( isFirefox ) return "Firefox";
    var isChrome = !isSafari && testCSS('WebkitTransform');  // Chrome 1+
    if ( isChrome ) return "Chrome";
    var isOpera = !!(window.opera && window.opera.version);  // Opera 8.0+
    if ( isOpera ) return "Opera";
    var isSafari = Object.prototype.toString.call(window.HTMLElement).indexOf('Constructor') > 0;
    if ( isSafari ) return "Safari";
    // At least Safari 3+: "[object HTMLElementConstructor]"
    return "Other";

    function testCSS(prop) {
        return prop in document.documentElement.style;
    }
}

document.write(retornar_navegador ());

Using pure JavaScript to detect browsers in a reliable way.
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