In this paper, we define a dual matrix for dual bicomplex numbers in dual 4-space. By using this new dual matrix, we define a new dual motion and it is proven that this dual motion is homothetic. We provide some theorems for dual velocities, dual pole points, and dual pole curves for this one parameter dual homothetic motion. Moreover, we demonstrate that the motion described by the regular order  dual curve has only one acceleration center of order  at every t-instant after defining dual accelerations