Cognitive radio technology can get used to mitigate spectrum scarcity in a wide range of wireless systems. The key factor in cognitive radio systems is to use a blind and reliable sensing method. Maximum to minimum eigenvalue (MME) is known as one of the best performing covariance based spectrum sensing methods in the literature. In this paper, we propose to use consecutive results of previously sensed signals in detection process to increase the performance of MME in a high range and introduce consecutive results MME (CRMME) method which is considerably more reliable with the cost of delay in secondary users communication. Simulations results are presented to verify the performance and effectiveness of the proposed CRMME method.