In this paper we present a new bit reversal algorithm which outperforms the existing ones. The bit reversal technique is involved in the fast Fourier transform technique (FFT), which is widely used in computer‐based numerical techniques for solving numerous problems. The new approach for computing the bit reversal is based upon a pseudo‐semi‐group homomorphism property. The surprise is that this property is almost trivial to prove but at the same time it also leads to a very efficient algorithm which we believe to be the best with only 𝒪 (N) operations and optimal constant, i.e. unity. Copyright © 2002 John Wiley & Sons, Ltd.