We define a new class of unitary solutions to the classical Yang-Baxte
r equation (CYBE). These 'boundary solutions' are those which lie in t
he closure of the space of unitary solutions of the modified classical
Yang-Baxter equation (MCYBE). Using the Belavin-Drinfel'd classificat
ion of the solutions to the MCYBE, we are able to exhibit new families
of solutions to the CYBE. In particular, using the Cremmer-Gervais so
lution to the MCYBE, we explicitly construct for all n greater than or
equal to 3 a boundary solution based on the maximal parabolic subalge
bra of sl(n) obtained by deleting the first negative root. We give som
e evidence for a generalization of this result pertaining to other max
imal parabolic subalgebras whose omitted root is relatively prime to n
. We also give examples of nonboundary solutions for the classical sim
ple Lie algebras.