The trick is to go through the array from end to beginning, so you don't mess up the indices while removing elements.
var deleteMe = function( arr, me ){
var i = arr.length;
while( i-- ) if(arr[i] === me ) arr.splice(i,1);
}
var arr = ["orange","red","black", "orange", "white" , "orange" ];
deleteMe( arr , "orange");
arr is now ["red", "black", "white"]