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An implementation of the reverse Monte Carlo algorithm is presented for the study of amorphous tetrahedral semiconductors. By taking into account a number of constraints that describe the tetrahedral bonding geometry along with the radial distribution function, we construct a model of amorphous silicon using the reverse Monte Carlo technique. Starting from a completely random configuration, we generate a model of amorphous silicon containing 500 atoms closely reproducing the experimental static structure factor and bond angle distribution and in improved agreement with electronic properties. Comparison is made to existing reverse Monte Carlo models, and the importance of suitable constraints beside experimental data is stressed.