In this work, we present an improvement to a well-known approximate methodology for solving the multi-dimensional time-dependent Schrodinger equation (TDSE). This approximation is the time-dependent Hartree (TDH) approximation which enforces the time-dependent wave-function remains factorized for all time. If the initial wavefunction of the system contains a term which couples two or more spatial coordinates then the TDH can not be invoked because the wave function can not be written in factorized form. In our work, it is shown how the TDH approximation can be invoked in such a case by decoupling the initially couple term in the wavefunction so that the wave function can be written in factorized form for all time. We also show how such a decoupling scheme can be used to perform the TDH approximation in an optimal rotated coordinate system where the coupling between spatial degrees of freedom in the potential energy is minimized.