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A new methodology has been recently proposed for the efficient generation of multiple pseudo-random bit sequences that are statistically uncorrelated [R. Kuehnel, March 2003]. Random sequences that are uniformly distributed over a range [0,K], where K+ 1 is a power of 2, can be constructed by forming a vector of M independent bit sequences, where M = log/sub 2/(K + 1). In this paper we demonstrate that this method of construction represents a special case of a more generalized approach in which K can be any positive integer. The procedures described here can be used to efficiently generate multiple independent random sequences that are uniformly distributed over any range.