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Magnetothermal instability may affect the performance of high critical current density Nb3Sn strands by quenching the superconductor at current values lower than its critical current. This phenomenon has important implications in the design of next-generation superconducting magnets for accelerators. According to the theory, the strand magnetothermal stability can be improved by changing the current distribution within the strand. In this paper, a technique to improve the conductor stability is presented. It consists in partially cutting the strand's outer superconducting subelements in the region where the wire is soldered to the copper block that feeds the current. The special cut forces the current to enter into the inner subelements without degrading the current capacity. As a consequence, the stability is increased, which avoids changing the strand critical current or its residual resistivity ratio because current redistribution during an external perturbation is strongly reduced. The experimental results obtained by applying this technique on a 0.8-mm restacked-rod process strand are presented and discussed.