  We consider the action of a subtorus of the big torus on a toric variety. The
aim of the paper is to define a natural notion of a quotient for this setting
and to give an explicit algorithm for the construction of this quotient from
the combinatorial data corresponding to the pair consisting of the subtorus and
the toric variety. Moreover, we study the relations of such quotients with good
quotients. We construct a good model, i.e. a dominant toric morphism from the
given toric variety to some ``maximal'' toric variety having a good quotient by
the induced action of the given subtorus.
