  We calculate, in the continuum limit of quenched lattice QCD, the form factor
that enters the decay rate of the semileptonic decay B --> D* l nu. By using
the step scaling method (SSM), previously introduced to handle two scale
problems in lattice QCD, and by adopting flavor twisted boundary conditions we
extract F(w) at finite momentum transfer and at the physical values of the
heavy quark masses. Our results can be used in order to extract the CKM matrix
element Vcb by the experimental decay rate without model dependent
extrapolations. The value of Vcb agrees with the one obtained from the B --> D
l nu channel and makes us confident that the quenched approximation well
applies to these transitions.
