In this paper, a genetic algorithm (GA) with local search is proposed for the unrelated parallel machine scheduling problem with the objective of minimising the maximum completion time (makespan). We propose a simple chromosome structure consisting of random key numbers in a hybrid genetic-local search algorithm. Random key numbers are frequently used in GAs but create additional difficulties when hybrid factors are implemented in a local search. The best chromosome of each generation is improved using a local search during the algorithm, but the better job sequence (which might appear during the local search operation) must be adapted to the chromosome that will be used in each successive generation. Determining the genes (and the data in the genes) that would be exchanged is the challenge of using random numbers. We have developed an algorithm that satisfies the adaptation of local search results into the GAs with a minimum relocation operation of the genes' random key numbers - this is the main contribution of the paper. A new hybrid approach is tested on a set of problems taken from the literature, and the computational results validate the effectiveness of the proposed algorithm.