Highscore GUI not working properly help

I've manage to set and show a score after the player game is over, only thing wrong is when i ever beat the highest score, it doesn't show "New Highscore" it shows "Score:(Number of points earn during the game)". I want it to display New Highscore whenever the player beats their highscore, if you can help me with this thank you!

 public GUIText scoreText;
     int score;
     int highScore;
     bool newHighScore;
     
     void Start ()
     {
         score = PlayerPrefs.GetInt ("Score");
         
         if (!PlayerPrefs.HasKey("HighScore")) {
             PlayerPrefs.SetInt("HighScore", score);
             newHighScore = true;
             highScore = score;
         }
         else {
             highScore = PlayerPrefs.GetInt("HighScore");
             if (score > highScore) {
                 newHighScore = true;
                 PlayerPrefs.SetInt("HighScore", score);
                 highScore = score;
             }        
             else
                 newHighScore = false;
         }
             
 
     }


          public void AddScore (int newScoreValue)
     {
         score += newScoreValue;
         UpdateScore ();
     }
     
     void UpdateScore ()
     {
         scoreText.text = "Score: " + score;
     }



 if (playerLives == 0 && player == null) 
         {
             GameOver();
             if (newHighScore)
                 GUI.Label (new Rect (Screen.width / 2 - 100, Screen.height / 2 - 10, 500, 100), "New High Score: " + score, "label");
             else
                 GUI.Label (new Rect (Screen.width / 2 - 100, Screen.height / 2 - 10, 500, 100), "SCORE: " + score, "label");
         }