A higher trapped field B T P and larger total trapped flux È T have been achieved on a SmBaCuO bulk superconductor ( 45 mm) by a modified multipulse technique with stepwise cooling (MMPSC) and a subsequent iterative magnetizing operation with gradually reduced pulse field amplitude (IMRA). B T P ¼ 4:33 T has been realized at the center of the bulk surface by the MMPSC method, which is higher than that attained by a single-pulse application (B T P ¼ 3:3 T). After the IMRA process, È T (5 mm) = 1.55 mWb was achieved 5 mm above the bulk surface, which is about 35% larger than that after the MMPSC process. The MMPSC method combined with the IMRA process (MMPSC-IMRA) is demonstrated to be a universal and promising pulse-field magnetization technique for enhancing both B T P and È T on any superconducting bulks.