Removing a Marker in Google Maps API v3

I'm trying to remove a marker that was initialized like this:

marker = new google.maps.Marker({
    position: latLng,
    map: map,
    draggable: true,
    animation: google.maps.Animation.DROP,
    title: 'Marker 1',
    icon: redPin
});

google.maps.event.addListener(marker, "click", function() {
    showMarkerDialog(marker.position, "marker");
});

google.maps.event.addListener(marker, "dblclick", function() {
    // Add a alert: Are you sure you want to remove this marker?

    map.removeOverlay(marker);
});

Everything works perfectly except that when I double click it to remove what I get on the Error Console is this:

TypeError: Object # has no method 'removeOverlay'

What am I doing wrong?