The power of Lawley-Hotelling (LH) type criterion is compared with those of likelihood ratio (LR) type, Bartlett-Nanda-Pillai's (BNP) type and largest root criteria. When the sample size is not so large, the power of LH criterion is locally optimum. However, when sample size is large, the power of LH is almost equivalent to that of LR type or BNP type criterion.