For the purpose of equalisation of rapidly time variant multipath channels, we derive a novel adaptive algorithm, the amplitude banded LMS (ABLMS), which implements a non-linear adaptation based on a coefficient matrix. Then we develop the ABLMS algorithm as the adaptation procedure for a linear transversal equaliser (LTE) and a decision feedback equaliser (DFE) where a parallel adaptation scheme is deployed. Computer simulations demonstrate that with a small increase of computational complexity, the ABLMS based parallel equalisers provide a significant improvement related to the conventional LMS DFE and the LMS LTE in the case of a second order Markov communication channel model.