The design of a class of jitter-robust, Hermite polynomial-based, orthogonal pulses for ultra-wideband impulse radio (UWB-IR) communications systems is presented. A unified and exact closed-form expression of the auto- and cross-correlation functions of Hermite pulses is provided. Under the assumption that jitter values are sufficiently smaller than pulse widths, this formula is used to decompose jitter-shifted pulses over an orthonormal basis of the Hermite space. For any given jitter probability density function (pdf), the decomposition yields an equivalent distribution of N -by- N matrices which simplifies the convolutional jitter channel model onto a multiplicative matrix model. The design of jitter-robust orthogonal pulses is then transformed into a generalized eigendecomposition problem whose solution is obtained with a Jacobi-like simultaneous diagonalization algorithm applied over a subset of samples of the channel matrix distribution. Examples of the waveforms obtained with the proposed design and their improved auto- and cross-correlation functions are given. Simulation results are presented, which demonstrate the superior performance of a pulse-shape modulated (PSM-) UWB-IR system using the proposed pulses, over the same system using conventional orthogonal Hermite pulses, in jitter channels with additive white Gaussian noise (AWGN).