How to create a true 'Random' with Timer control?

I have a timer that clicks a button, and no matter what speed the timer is at, due to the Random having some kind of association with the clock, the outcome is predictable no matter what the speed.

I have been reading up and learned that when a new Random is initialized, it is done so with the system time, which explains why I'm getting this problem.

Here's what I have:

   int win = 0;
   int lose = 0;

    private void button1_Click(object sender, EventArgs e)
    {
        Random rn = new Random();
        int rnu = rn.Next(2);

        if (rnu == 0)
            win++;

        if (rnu == 1)
            lose++;

          string winmsg = "Wins: " + win.ToString();
          string losemsg = "Losses: " + lose.ToString();

        winlbl.Text = winmsg;
        loselbl.Text = losemsg;

        timer1.Start();

    }

And then the timer:

    private void timer1_Tick(object sender, EventArgs e)
    {
        button1.PerformClick(); //interval 500, but always predictable.
    }

My goal is to try to create a more 'Random' outcome- one that wouldn't be predictable with the timer control. However, I can't modify the speed of the timer; it must remain constant for the cycle.

I've tried stopping the timer and restarting, but even then it carries on the predictable behavior.

Does anyone know of a way to get around this or some kind of 'trick'? Or is this some C# Random limitation?