a b s t r a c tA method to produce spin-aligned rare isotope (RI) beams has been developed, where a scheme of twostep projectile fragmentation to produce the RI of interest with high spin alignment and a technique of momentum-dispersion matching are combined. Effectiveness of the present method was demonstrated in an experiment at the RIKEN RIBF, where an RI beam of 32 Al with spin alignment of 8(1)% was successfully produced from a primary beam of 48 Ca, via an intermediate RI of 33 Al. Figure of merit of the present method was found to be more than 50 times greater than that of the conventional method employing single-step projectile fragmentation.