This report describes the results of an empirical study to develop a normalizing transformation for sample multiple coherence. The 'Fisher z- transformation' is employed. The expected value (including a bias term) and variance of the transformation have been experimentally determined. Numerical values of the transformation which is developed (including the bias term and variance) may be obtained with a reasonable amount of computation. Tables of the Gaussian distribution can then be used to obtain confidence limits and perform statistical tests. The computational methods and the digital computer program used for the study are described in detail. Flow charts of the program are given. Numerical results from the program results are presented. Examples of the use of the transformation are given for developing confidence limits for multiple coherence. A recommendation for a further theoretical study is presented.