Cooperative spectrum sensing based on the limiting eigenvalue ratio of the covariance matrix offers superior detection performance and overcomes the noise uncertainty problem. While an exact expression exists, it is complex and multiple useful approximate expressions have been published in the literature. An improved, more accurate, integral solution for the probability density function of the ratio is derived using order statistical analysis to remove the simplifying, but incorrect, independence assumption. Thereby, the letter makes an advance in the rigorous theory of eigenvalue-based spectrum sensing.