  The exact quantum $S$-matrices and conserved charges are known for affine
Toda field theories(ATFTs). In this note we report on a new type of bi-linear
sum rules of conserved quantities derived from these exact $S$ matrices. They
exist when there is a multiplicative identity among $S$-matrices of a
particular ATFT. Our results are valid for simply laced as well as non-simply
laced ATFTs. We also present a few explicit examples.
