  We consider nonquasiclassical solutions to the quantum Yang-Baxter equation
and the corresponding quantum cogroups $\Fun(SL(S))$ constructed earlier by one
of the authors . We give a criterion of the existence of a dual quasitriangular
structure in the algebra $\Fun(SL(S))$ and describe a large class of such
objects related to the Temperley-Lieb algebra satisfying this criterion. We
show also that this dual quasitriangular structure is in some sense
nondegenerate.
