We consider the isobaric-isothermal molecular dynamics method in a system subject to a set of holonomic constraints with a full atomic description of the virial. By applying the non-Hamiltonian statistical mechanical theory recently developed by Tuckerman et al. [Tuckerman, M. E.; Mundy, C. J.; Martyna, G. J. Europhys. Lett. 1999, 45, 149], the Kneller-Mulders equations [Kneller, G. R.; Mulders, T. Phys. Rev. E 1996, 54, 6825] are analyzed, and it is determined that they sample the desired ensemble only under certain circumstances. In general. a bias arising from the conservation of total momentum needs to be corrected. Thus, a new set of equations of motion is presented and the phase space generated by these equations is shown to be correct under all circumstances.