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In this paper the independence between a block of natural parameters and the complementary block of mean value parameters holding for densities which are natural conjugate to some regular exponential families is used to design in a convenient way a Gibbs' sampler with block updates. Even when the densities of interest are obtained by conditioning to zero a block of natural parameters in a density conjugate to a larger``saturated'' model, the updates require only the computation of marginal distributions under the``unconditional'' density. For exponential families which are closed under marginalization, including both the zero mean Gaussian family and the cross-classi®ed Bernoulli family such an implementation of the Gibbs' sampler can be seen as an Iterative Proportional Fitting algorithm with random inputs.

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