The BIPF algorithm is a Markovian algorithm with the purpose of simulating certain probability distributions supported by contingency tables belonging to hierarchical loglinear models. The updating steps of the algorithm depend only on the required expected marginal tables over the maximal terms of the hierarchical model. Usually these tables are marginals of a positive joint table, in which case it is well known that the algorithm is a blocking Gibbs Sampler. But the algorithm makes sense even when these marginals do not come from a joint table. In this case the target distribution of the algorithm is necessarily improper. In this paper we investigate the simplest non trivial case, i. e. the 2 £ 2 £ 2 hierarchical interaction. Our result is that the algorithm is asymptotically attracted by a limit cycle in law.
