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Electrical edge joint of a stacked high-temperature superconducting (HTS) conductor is explored for electrical joints for a demountable HTS toroidal field coil. Demountable coils would be very useful in small tokamak plasma-facing component-test machines, such as Vulcan. The demountable concept explored in this paper consists of forcing together the edges of stacked HTS conductor embedded in a conductive or a structural material. We carried out a testing program of the edge joint of a stacked YBCO conductor within a copper jacket. The HTS cable has a critical current of 1600 A at 77 K in self-field. The experimental results showed that joint resistance in the edge joint was higher than expected, as was not reproducible. One potential reason for the larger than expected resistance is the damage to the tape edge in preparation of the joint region due to milling/fabrication. Another potential reason was low accuracy in the fabrication of joint surface; the joint surfaces were not parallel to one another. The joint resistance will be reduced by the sophistication of the fabrication process for the joint surface. We also carried out calculations to determine the joint performance of the edge joint in an ideal condition. In the ideal condition, inserting an indium film between joint surfaces or plating copper layer on joint surfaces can prevent joint resistance from increasing due to the misalignment of the contact surfaces and would provide a compliant layer between joints. The joint resistance of the edge joint can become smaller than that of an electrical lap joint when the number of the stacked HTS tape is large.