To enhance the error performance of impulse radio UWB transceivers, we introduce in this manuscript a novel modulation scheme based on exploiting the symmetry properties of transmitted waveforms. Parity Modulation utilizes odd versus even pulses to represent binary data, while the detector relies on a time reverser and non-coherent cross correlator. The analytical expression of power spectral density has been derived; then, considering different orders of Gaussian derivatives as pulse waveforms, the spectral characteristics have been optimized to comply with the UWB emission regulation. The bit error rate formula in an AWGN channel has been developed, while our simulation measurements showed a significant performance gain for 2 Gbps Parity over 1 Gbps Pulse Position Modulation and 2 Gbps On Off Keying. A reference-based parity scheme has been eventually proposed to enhance robustness against multi-path effects, interesting results have been achieved in terms of error probability in a realistic channel, with a compromise between data rate and complexity.