Bestle and Zeitz have introduced a non-linear time-variable observer canonical form which permits, through a non-linear state transformation, the use of the eigenvalue assignment method to design observers for non-linear time-variable dynamic systems. In this paper, a necessary and sufficient condition under which the transformation exists is given. It is also proved that the transformation could be determined by integrating single variable functions instead of solving a set of partial differential equations as shown by Bestle and Zeitz. Examples are included to show how to do the transformation.