  We carefully perform a Hamiltonian Dirac's constraint analysis of
$\omega=-\frac{3}{2}$ Brans-Dicke theory with Gibbons-Hawking-York (GHY)
boundary term. The Poisson brackets are computed via functional derivatives.
After a brief summary of the results for $\omega\neq-\frac{3}{2}$ case, we
derive all Hamiltonian Dirac's constraints and constraint algebra both in the
Jordan and Einstein frames. Confronting and contrasting Dirac's constraint
algebra in both frames, it is shown that they are not equivalent. This
highlights the transformations from the Jordan to the Einstein frames are not
Hamiltonian canonical transformations.
