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In this paper, we propose a new modulation scheme called biorthogonal pulse position modulation (BPPM) for ultra-wideband (UWB) communication systems. A set of N=2k+1 BPPM signals are constructed from 2k orthogonal PPM signals by including the antipodal version of the orthogonal PPM signals. The channel capacity of BPPM is determined for a time-hopping multiple access UWB communication system. The error probability and performance bounds are derived for a multiuser environment. It is shown that N-ary BPPM has better performance than N-ary PPM with the same throughput and half the computational complexity.