  We continue to study the spherically symmetric vacuum solutions of the
tensor-four-scalars theory which is a modification of general relativity. Our
aim is to construct vacuum solutions with asymptotically constant circular
velocity curves which can be used to represent the dark halo outside the
baryonic matter. These solutions are obtained by means of a new non-standard
gauge in the field equations. The metric is expressed in terms of the rotation
curve $V(r)$ in closed form.
