  We prove that any globally periodic rational discrete system in K^k(where K
denotes either R or C), has unconfined singularities, zero algebraic entropy
and it is complete integrable (that is, it has as many functionally independent
first integrals as the dimension of the phase space). In fact, for some of
these systems the unconfined singularities are the key to obtain first
integrals using the Darboux-type method of integrability.
