  We study residues on a complete toric variety X, which are defined in terms
of the homogeneous coordinate ring of X. We first prove a global transformation
law for toric residues. When the fan of the toric variety has a simplicial cone
of maximal dimension, we can produce an element with toric residue equal to 1.
We also show that in certain situations, the toric residue is an isomorphism on
an appropriate graded piece of the quotient ring. When X is simplicial, we
prove that the toric residue is a sum of local residues. In the case of equal
degrees, we also show how to represent X as a quotient (Y-{0})/C* such that the
toric residue becomes the local residue at 0 in Y.
