A minor, but crucial, modification to the original version of the TM was recently proposed in order to ensure that the model predictions were entirely consistent with those of the phenomenological theory of martensite crystallography (PTMC). In the present paper an analysis based on the principles of the Frank-Bilby equation is used to derive this modified version of the two-dimensional TM equation for the habit plane orientation from first principles. A considerably simpler and more accurate expression for the tilt rotation is also presented. Finally, a simple method for using the TM approach to calculate the shape strain, its magnitude and direction is described. The results of the predictions made with this improved version of the TM are compared with those of the original TM and with the corresponding PTMC predictions.