Using a named mutex to lock a file

I'm using a named mutex to lock access to a file (with path 'strFilePath') in a construction like this:

private void DoSomethingsWithAFile(string strFilePath)
{
      Mutex mutex = new Mutex(false,strFilePath.Replace("\\",""));
      try
      {
         mutex.WaitOne();
         //do something with the file....
      }
      catch(Exception ex)
      {
         //handle exception
      }
      finally
      {
         mutex.ReleaseMutex();
      }
 }

So, this way the code will only block the thread when the same file is being processed already. Well, I tested this and seemed to work okay, but I really would like to know your thoughts about this.