Let (X,Y) be a random variate with bivariate normal distribution. We are frequently interested in testing statistical hypotheses concerning the correlation coefficient between X and Y irrespective of their means and variances. However, small sample sequential procedures for this problem have not been found, to the author's knowledge, and the problem is usually reduced to a simpler one by assuming certain information concerning the variances of X and Y. For example, it may be assumed the X and Y have equal unknown variances. The problem, with these assumptions, still pose some difficulties and only few solutions are offered in the literature, namely those given by Wald (1947), Cox (1952), and Choi (1971). Wald used a weight function approach to integrate out our ignorance of parameters other than the correlation coefficient . Generally there are several choices for the weight function and it is not known what properties the test has. Cox's procedure transform the original observations to a new set of observations their distribution depends only on .