This paper examines asymptotic distributions of the canonical correlations between and with q<=p, based on a sample of size of N=n+1. The asymptotic distributions of the canonical correlations have been studied extensively when the dimensions q and p are fixed and the sample size N tends toward infinity. However, these approximations worsen when q or p is large in comparison to N. To overcome this weakness, this paper first derives asymptotic distributions of the canonical correlations under a high-dimensional framework such that q is fixed, m=n-p-->[infinity] and c=p/n--c0[set membership, variant][0,1), assuming that and have a joint (q+p)-variate normal distribution. An extended Fisher's z-transformation is proposed. Then, the asymptotic...</=p,>