Save Timer HighScore

I have a script, which has a timer and i want to make a highscore system for that timer. I have already made a script but it won't save the highscore. It only updates the score, so if the score is 45 seconds, the best will be 45 seconds and then if it is 65 seconds the next time, it will update to 65 seconds. But it isn't supposed to, because 65 seconds is slower than 45 seconds. Anyone who knows what is wrong?

Here is the script.

 var bestTime : int = 0;
 var completeTime : int = 0;
 
 static var gameTimeAllowed : float = 60.0;
 static var gameTimeRemaining : float = gameTimeAllowed;
 
 function Start() {
 
  bestTime = PlayerPrefs.GetInt("bestTime",bestTime);
 
 }
 
 function Update() { 
    
        completeTime = gameTimeAllowed - gameTimeRemaining;
    
       if(bestTime < completeTime){
       bestTime = completeTime;
       PlayerPrefs.SetInt("bestTime",bestTime);
     }
     
 }
 
 function OnGUI() {
 
 
          GUI.Label(Rect(Screen.width/2-80,Screen.height/2-130,300,100),"Best Time : " +  bestTime.ToString() + " Seconds");
 
 }