One of the methods of unifying the global positioning system (GPS) velocity fields (VFs) of tectonic motions is based on the Eulerian vector (EV) estimation. In this method the difference between each available local VF and a reference VF (REF) is derived and an EV is estimated for the differences in a least-squares sense. After that each local VF is unified with respect to REF using the EV. The classical approach to the EV determination is nonlinear and requires the approximate EV. To solve this problem a simple linear approach is developed in this paper for estimating the EV and applied for unifying the existing local VFs in Iran. Our approach is free of the approximate parameters of the EV, faster and more efficient than the classical one. Here, both of the classical and the new approaches are numerically applied and compared to each other; and used to unify the VFs covering a large part of Iran. The unified velocity field shows an overall northward motion with respect to Eurasia with a convergence pattern around the southern Caspian Basin and a little divergence in the central and southern areas.