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In this work, a non-spontaneous martensitic transformation (MT) activated by the hydrostatic pressure has been observed in polycrystalline Ni43Co7Mn35In15 Heusler alloy. This alloy can experience a nearly complete metamagnetic MT with the assistance of an enough pressure. As the change of pressure reaches 20 kbar, the maximum baroresistance (BR) of the studied alloy achieves ~ 825% at 50 K and remains ~ 280% even in the vicinity of room temperature revealing a giant BR effect over a wide temperature range. More interestingly, the perfectly reversible isothermal BR effects as high as over 650% have been also found at the temperatures below 130 K by overcoming a thermal barrier between direct and reverse MTs. Such an interesting behavior could be ascribed to a pressure-induced continuous first-order MT accompanied by a prominent change of spin ordering, which brings about a combined contribution of electron-spin and electron-lattice scatterings. [ABSTRACT FROM AUTHOR]