We study a simple reaction-diffusion process that exhibits a phase transition to an absorbing phase in its steady state. We characterize the universal properties of the transition by computing the associated critical exponents. We suggest that the exclusion constraint between particles may change the universality class of the transition even though the density is asymptotically low at the transition. This is surprising as no segregation or jamming phenomena are in play since we are dealing with a single species diffusing without drift.