In this letter, we consider the multiantenna spectrum sensing for correlated signal in a cognitive radio network, where uncalibrated multiple antennas are employed at the secondary user to detect the presence of the primary user (PU). Under such a scenario, we demonstrate that the correlation function matrices of the received signals differ between the null hypothesis and the alternative hypothesis, which can be leveraged to probe the state of PU. Based on this, a correlation-based local average variance (CLAV) detection method is proposed to exploit the correlated property of the primary signals. Also, its asymptotic distribution under the null hypothesis is derived with the aid of the central limit theorem, which enables us to theoretically obtain the decision threshold of the CLAV method. Finally, we carry out the simulation results to illustrate the superior performance of proposed method compared to the conventional methods.