  We find a new braided Hopf structure for the algebra satisfied by the entries
of the braided matrix $BSL_q(2)$. A new nonbraided algebra whose coalgebra
structure is the same as the braided one is found to be a two parameter
deformed algebra. It is found that this algebra is not a comodule algebra under
adjoint coaction. However, it is shown that for a certain value of one of the
deformation parameters the braided algebra becomes a comodule algebra under the
coaction of this nonbraided algebra. The transmutation of the nonbraided
algebra to the braided one is constructed explicitly.
