JS: Most optimized way to remove a filename from a path in a string?

I have strings formatted as follows:
path/to/a/filename.txt

Now I'd like to do some string manipulation which allows me to very efficiently remove the "filename.txt" part from this code. In other words, I want my string to become this:
path/to/a/

What's the most efficient way to do this? Currently I'm splitting the string and reconnecting the seperate elements except for the last one, but I get the feeling this is a really, REALLY inefficient way to do it. Here's my current, inefficient code:

res.getPath = function(file)
{
  var elem = file.split("/");
  var str = "";
  for (var i = 0; i < elem.length-1; i++)
    str += elem[i] + "/";
  return str;
}

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