A common practice in Monte Carlo radiation transport codes is to start each random walk a specified number of steps up the random number sequence from the previous one. This is called the stride in the random number sequence between source particles. It is used for correlated sampling or to provide tree-structured random numbers. A new random number generator algorithm for the major Monte Carlo code MCNP has been written to allow adjustment of the random number stride. This random number generator is machine portable. The effects of varying the stride for several sample problems are examined.