  In this paper we investigate Lie bialgebra structures on the
Schr\"odinger-Virasoro algebra $\LL$. Surprisingly, we find out an interesting
fact that not all Lie bialgebra structures on the Schr\"odinger-Virasoro
algebra are triangular coboundary, which is different from the related known
results of some Lie algebras related to the Virasoro algebra.
