Singletonize revisited

For some reason, yesterday night while musing about how the [[prototype]] (accessible via __proto__ in Firefox and Chrome) and prototype work (I think I've finally fully understood it after all theses years in which I was missing some details) it came to my mind a post that I published 1 year ago.
After refreshing my mind reading the article, and in light of my improved JavaScript skills, I have to say that the solution there was overcomplicated, and can be replaced with something utterly more simple:

function singletonize(initialFunc){
 if (initialFunc._singletonized)
  return initialFunc;
 
 //this is the new  constructor that will replace the initial one and that we'll return
 var singletonized = function(){
  if (initialFunc._singletonInstance)
   return initialFunc._singletonInstance;
  else{
   //just call the initial constructor with the this object that has been passed to the singletonized contructor
   initialFunc.apply(this, arguments);
   initialFunc._singletonInstance = this;
   return initialFunc._singletonInstance;
  }
 };
 //essential to make the prototype thing work
 singletonized.prototype = initialFunc.prototype;
 
 initialFunc._singletonized = true;
 return singletonized;
}

Find the whole code here