This transformation method from Box and Muller, known as the Polar method, is based on the following procedure:

Assuming and are two standard random numbers. Set

If applies, the random numbers

are independent standard normally distributed random numbers. If the condition does not apply, two new standard random numbers and are generated, which are independent of and . The algorithm is then executed again with these figures.

With this procedure you require two standard random numbers to generate two -distributed random numbers if the condition is met. The probability of this condition being met is , so that on average standard random numbers are needed.