Within CERN the development of REBCO-CORC (Conductor On Round Core) type cables is pursued in view of possible application in future detector and accelerator magnets. An important issue is the design and qualification of terminations for connecting CORC cables mutually or to bus-bars. A termination design is envisaged that combines a simple manufacturing process with a lowest possible joint terminal resistance in the few nΩ range at 4.2 K, first for a single CORC cable and subsequently for CORC based Cable-in-Conduit Conductors. The investigation concerns the effect of tapering the CORC cable within the joint to form a staircase like geometry, which allows current to pass more directly from the copper joint casing to the inner REBCO layers of the CORC cable. Simulations have shown a substantial decrease in joint resistance at operating current in the case both CORC cable and joint casing are tapered. The CORC cable and new joint were tested at CERN. In this paper, some details of the new joint design, fabrication process, and model are presented and the results are summarized.