Inter-cell interference (ICI) in Large Scale Antenna Systems, resulted from pilot contamination, bounds the system performance in the infinite antenna regime. A new concept, pilot contamination precoding (PCP), was recently proposed to cancel ICI. The main idea of PCP is that base stations linearly combines messages aimed to terminals from different cells. Crucially, the coefficients depend only on the slow fading coefficients. In this work we consider PCP for the finite antenna regime, where three other types of interference become prominent. We formulate the PCP design as maximizing SINR subject to power constraint and propose algorithms for solving this problem. With M=100 base station antennas PCP gives, very significant, about 400 times, improvement in data transmission rate.