  We construct a mutually catalytic branching process on a countable site space
with infinite "branching rate". The finite rate mutually catalytic model, in
which the rate of branching of one population at a site is proportional to the
mass of the other population at that site, was introduced by Dawson and Perkins
in [DP98]. We show that our model is the limit for a class of models and in
particular for the Dawson-Perkins model as the rate of branching goes to
infinity. Our process is characterized as the unique solution to a martingale
problem. We also give a characterization of the process as a weak solution of
an infinite system of stochastic integral equations driven by a Poisson noise.
