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We report effect of hydrostatic pressure on martensitic transformation in polycrystalline Ni 44.6 Co 5.5 Mn 35.5 In 14.4 . With applying pressure, the transformation moves to high temperatures at a rate of 4.4 K/kbar. Utilizing an indirect method, the calculated maximum isothermal entropy changes achieve ~ 14.3 J/kg K at 2.76 kbar and ~ 15.6 J/kg K at 5.98 kbar, which respectively output the values of ~ 5 K and ~ 6 K for the adiabatic temperature change near room temperature. After deducting the average hysteretic loss (~ 152 J/kg), the effective refrigeration capacities still reach ~ 38 J/kg at 2.76 kbar and ~ 247 J/kg at 5.98 kbar, performing an enhanced barocaloric effect. [ABSTRACT FROM AUTHOR]