A Bayesian procedure for examining whether the time-space variation of the magnitudefrequency relation conforms with the exponential distribution or not is proposed. The relation in each time-space segment is obtained as a histogram. The smoothness of the estimated histogram is guaranteed by the introduction of prior distributions of the parameters in time, space, and magnitude. The parameters of the prior distribution are chosen to minimise Akaike's Bayesian Information Criterion (ABIC). This procedure is applied to three earthquake catalogues in New Zealand: those for the Wellington Seismograph Network, the Pukaki Network, and the New Zealand Network respectively. For both the Wellington and Pukaki Networks, departure from the exponential distribution is the main effect and the time variation is secondary. For the New Zealand Network, where the magnitude- frequency relation appears to be an exponential distribution, the variation of b over time and space suggests a relation between periods of active seismicity and periods of high b-value, not locally, but overall in the main seismic region.