The limited number of pixels and their quantized phase modulation values limit the positioning accuracy when a phase-only one dimensional spatial light modulator (SLM) is used for beam steering. Applying the straightforward recipe for finding the optimal setting of the SLM pixels, based on individually optimizing the field contribution from each pixel to the field in the steering position, the inaccuracy can be a significant fraction of the diffraction limited spot size. This is especially true in the vicinity of certain steering angles where precise positioning is particularly difficult. However, by including in the optimization of the SLM setting an extra degree of freedom, we show that the steering accuracy can be drastically improved by a factor proportional to the number of pixels in the SLM. The extra degree of freedom is a global phase offset of all the SLM pixels which takes on a different value for each steering angle. Beam steering experiments were performed with the SLM being set both according to the conventional and the new recipe, and the results were in very good agreement with the theoretical predictions.