An optically active .beta.-aminoalkoxyborane complex of the formula (I): ##STR1## wherein R.sup.1 is C.sub.1 -C.sub.8 alkyl, C.sub.3 -C.sub.7 cycloalkyl, C.sub.7 -C.sub.11 aralkyl or C.sub.6 -C.sub.10 aryl, R.sup.2 is hydrogen, C.sub.1 -C.sub.8 alkyl, C.sub.3 -C.sub.7 cycloalkyl or C.sub.7 -C.sub.11 aralkyl, or R.sup.1 and R.sup.2 together form (CH.sub.2).sub.n wherein n is 3 or 4, and Ar is naphthyl, anthryl or phenanthryl, which may be substituted by from 1 to 3 substituents selected from the group consisting of halogen, nitro, C.sub.1 -C.sub.6 alkyl, C.sub.3 -C.sub.7 cycloalkyl, C.sub.2 -C.sub.6 alkenyl, C.sub.2 -C.sub.6 alkynyl, C.sub.7 -C.sub.11 aralkyl, C.sub.6 -C.sub.10 aryl, C.sub.1 -C.sub.6 alkoxy and styrene polymer substituents.