In this paper, we present an improved precoding technique which reduces a modulo loss in vector perturbation (VP) with low complexity for the downlink of a multiuser multiple-input multiple-output (MIMO) system. At low SNR regime, the VP suffers from the modulo loss due to the increased number of nearest neighbors. For the original VP, the sphere encoder searches perturbation vectors in the infinite lattice. In contrast, the proposed scheme restricts the search range utilizing the distribution of the perturbation vector depending on transmitted data. As a result, we can achieve significant complexity savings at the transmitter and the receiver while providing better performance compared to the conventional sphere encoder. Simulation results show that the proposed scheme provides a 0.2 dB gain over the conventional VP at a bit error rate (BER) of 10-3 for the case of four transmit antennas and four users with 4QAM. Also, the proposed scheme reduces the maximum number of candidate search by 95% in comparison to the original VP.