  This paper provides a construction of a Fleming--Viot measure valued
diffusion process, for which the transition function is known, by extending
recent ideas of the Gibbs sampler based Markov processes. In particular, we
concentrate on the Chapman--Kolmogorov consistency conditions which allows a
simple derivation of such a Fleming--Viot process, once a key and apparently
new combinatorial result for P\'{o}lya-urn sequences has been established.
