  Chiriv\`{\i} and Maffei \cite{CM II} have proved that the multiplication of
sections of any two ample spherical line bundles on the wonderful symmetric
variety $X=\bar{G/H}$ is surjective. We have proved two criterions that allows
ourselves to reduce the same problem on a (smooth) complete symmetric variety
to the corresponding problem on the complete toric variety (respectively to the
open toric variety). We have also studied in details some family of complete
symmetric varieties, in particular those of rank 2.
