The coefficient alpha is the most widely used measure of internal consistency for composite scores in the educational and psychological studies. However, due to the difficulties of data gathering in psychometric studies, the minimum sample size for the sample coefficient alpha has been frequently debated. There are various suggested minimum sample sizes for the robust estimate of the population coefficient alpha. This research indicates that the performance of an estimator of the coefficient alpha depends not only on the sample size but also on the largest eigenvalue of the sample data set. Thus, when the largest eigenvalue increases, unbiased estimation of the population coefficient alpha is possible, even though the sample size is small. The simulations in this study were based on Monte-Carlo method with bootstrap technique. (Contains 2 tables and 4 figures.)