In this paper, we describe an alternative methodology for the assessment of global Terrestrial Reference Frames (TRFs), called the Velocity Decomposition Analysis (VEDA). Although it is related to the well-known Helmert transformation, a new conceptual manner is presented and discussed. All the necessary mathematical formulas for the adjustment and the quality assessment are provided, as well as a discussion of the similarities and differences to the existing approaches. The core of the VEDA concept lays on the separation of the velocities in two parts: the transformation related one and the optimal velocities, respectively. Using the suggested strategy, we test the global TRFs, the ITRF2008 and the DTRF2008. Their comparison in terms of Helmert transformation parameters reveals discrepancies reaching 0.83 mm/yr for the orientation rates, 0.97 mm/yr for the translation rates and 0.32 mm/yr for the scale rate. The comparison between the new approach and the classical Helmert transformation shows a consistency at the level of 0.66 mm/yr in a mean sense. In addition, we find a relative bias between the two frames reaching 0.44 mm/yr. The new approach also allows quantifying the geometric effect which corresponds to the impact of the systematic inconsistencies and the effect of the set of stations global distribution.