The Garey-Johnson algorithm is one of only two known polynomial-time algorithms allowing to construct an optimal schedule for the maximum lateness problem with unit execution tasks, two parallel identical processors, precedence constraints and release times. The paper is concerned with the worst-case analysis of a generalisation of the Garey-Johnson algorithm for the case of arbitrary number of processors. We prove that for even number of processors the algorithm is characterised by the best currently known performance guarantee, whereas for odd number of processors it is less competitive.