An efficient adaptation technique of the delay is introduced for accomplishing more accurate adaptive linear equalization of nonminimum phase channels. It is focused that the filter structure and adaptation procedure of the adaptive Butler-Cantoni (ABC) equalizer is very suitable to deal with a variable delay for each iteration, compared with a classical adaptive linear transversal equalizer (LTE). We derive a cost function by comparing the system mismatch of an optimum equalizer coefficient vector with an equalizer coefficient vector with several delay settings. The cost function is square of difference of absolute values of the first element and the last element for the equalizer coefficient vector. The delay adaptation method based on the cost function is developed, which is involved with the ABC equalizer. The delay is adapted by checking the first and last elements of the equalizer coefficient vector and this results in an LTE providing a lower mean square error level than the other LTEs with the same order. We confirm the performance of the ABC equalizer with the delay adaptation method through computer simulations.