The first-order superconducting transition, recently discovered in a long-standing candidate for a spin-triplet chiral-p-wave superconductor Sr2RuO4, is mysterious because it is not expected within the present scenario of spin-triplet superconductivity. To uncover its mechanism, we have measured the magnetization and the magnetic torque using an ultra-clean single crystal of Sr2RuO4 down to 0.1 K. In this study, the magnetic-field orientation has been controlled with a high precision within the accuracy of 0.01 degrees. We observed a sharp magnetization jump of as large as 0.01 emu/g with a field hysteresis of 100 Oe at 0.1 K. With increasing temperature, this magnetization jump decreases and diminishes above 0.8 K. The magnetic torque indicates that the first-order transition occurs only when the magnetic field is applied close to the ab plane within 2 degrees deviation. These features of the first-order transition provide the keystone issues whose resolution is crucial in uncovering a "hidden" pair-breaking mechanism within the triplet-pairing scenario, or might urge the reconsideration of the order parameter in Sr2RuO4. (C) 2015 Elsevier B.V. All rights reserved.