Despite there are many hybrid beamforming architectures and algorithms for multiuser Massive Multiple Input Multiple Output (MIMO) system in terrestrial networks, it is still in the initial stages for non-terrestrial networks. This research studies the system model of multiuser MIMO system for Satellite communications, investigates the channel model, and formulates the problem of hybrid beamforming. In essence, it proposes a novel hybrid beamforming algorithm designed for multiuser Massive MIMO systems. The proposed algorithm shows a significant gain in spectral efficiency and a considerable decrease in computation time. Moreover, the proposed algorithm maintains a similar spectral efficiency to continuous phase algorithms but reduces costs by using discrete phase shifters for the Radio Frequency (RF) chains rather than continuous counterparts. Numerical experiments exhibit the efficacy of our novel algorithm, surpassing recent algorithms in the field. Since our algorithm is compared with algorithms used for terrestrial communications and it is not restricted to LEO channel model, it can be applied for terrestrial and non-terrestrial communications.