i think i have my logic wrong

i have 2 arrays that generate random cities and post the cities to my applet...
this is all working fine..

but sometimes the applet will randomly generate two of the same cities
like: Miami Miami

here is my code
and i know my logic is wrong in my if loop

or maybe i dont need that index and index1 for the same array???

any suggestions
thanks in advance annie

Code:
import java.awt.*;
import javax.swing.*;
import java.util.*;

public class myAppletTest extends JApplet
{   
    private String arrLocal[] = new String[5];
    private String arrForeign[] = new String[3];
     
    Random rnd = new Random();
    int index = rnd.nextInt( arrLocal.length );
    String randomLocal = arrLocal[index];
        
    Random rnd1 = new Random();
    int index1 = rnd.nextInt( arrLocal.length );
    String randomLocal1 = arrLocal[index1];
    
    Random rnd2 = new Random();
    int index2 = rnd.nextInt( arrForeign.length );
    String randomForeign = arrForeign[index2];
    
    public void init()
    {
        arrLocal = new String[] { "New York", "Boston", "Miami", "Philadelphia", "Chicago" };
        arrForeign = new String[] {"Madrid", "London", "Paris"}; 
               
        for (int k = 0; k < arrLocal.length; k ++)
            System.out.println(arrLocal[k]);
           
        for (int i = 0; i < arrForeign.length; i ++)
            System.out.println(arrForeign[i]);
            
        if(arrLocal[index]==arrLocal[index1])
        {
            for (int k = 0; k < arrLocal.length; k ++)
            System.out.println(arrLocal[k]);        
        }
        
    }//end init()
    
    public void paint(Graphics g)
    {
        g.drawString( "We have special rates to: " , 5 , 30);
        g.drawString( arrLocal[index] , 5 , 45);
        g.drawString( arrLocal[index1] , 5 , 60);
        g.drawString( "Inexpenive vacations to: " , 5 , 90);
        g.drawString( arrForeign[index2] , 5 , 105);   
          
    }
}