  Let X be a smooth projective toric surface and L and M two line bundles on X.
If L is ample and M is generated by global sections, then we show that the
natural map from H^0(X,L) tensor H^0(X,M) to H^0(X, L tensor M) is surjective.
We also consider a generalization to the case when M is an arbitrary line
bundle with h^0(X,M) > 0.
