Employing the currently discussed notion of pseudo-hermiticity, we define a pseudo-unitary group. Further, we develop a random matrix theory which is invariant under such a group and call this ensemble of pseudo-Hermitian random matrices as the pseudo-unitary ensemble. We obtain exact results for the nearest-neighbour level spacing distribution for (2 × 2)-matrices which has a novel form, s log 1/s near zero spacing. This shows a level repulsion in marked distinction with an algebraic form s^β in the Wigner surmise. We believe that this paves way for a description of varied phenomena in two-dimensional statistical mechanics, quantum chromodynamics, and so on.