An adaptive blind equalisation algorithm for high‐order quadrature amplitude modulations is proposed. It is derived by combining the multi‐modulus criterion and a new alphabet‐matching penalty term. This penalty is based on the minimum ℓ1‐norm of the deviations of the equaliser output from the alphabet elements. Numerical experiments show that the proposed criterion provides higher performance in terms of residual error and convergence speed than the conventional multi‐modulus algorithm and its penalised versions. Copyright © 2012 John Wiley & Sons, Ltd.