  We study the stationary state of a simple exclusion process on a ring which
was recently introduced by Arndt {\it et al} [J. Phys. A {\bf 31} (1998)
L45;cond-mat/9809123]. This model exhibits spatial condensation of particles.
It has been argued that the model has a phase transition from a ``mixed phase''
to a ``disordered phase''. However, in this paper exact calculations are
presented which, we believe, show that in the framework of a grand canonical
ensemble there is no such phase transition. An analysis of the fluctuations in
the particle density strongly suggests that the same result also holds for the
canonical ensemble.
