The minimax algorithm, also called the negamax algorithm, remains today the most widely used search technique for two-player perfect-information games. However, minimaxing has been shown to be susceptible to game tree pathology, a paradoxical situation in which the accuracy of the search can decrease as the height of the tree increases. Althöfer’s alternative minimax algorithm has been proven to be invulnerable to pathology. However, it has not been clear whether alpha-beta pruning, a crucial component of practical game programs, could be applied in the context of Alhöfer’s algorithm. In this brief paper, we show how alpha-beta pruning can be adapted to Althöfer’s algorithm.