Spectrum sensing is without doubt the most important part in the implementation of cognitive radio networks. Therefore, many algorithms for signal detection of primary users have been proposed, being those based on spectral correlation the most outstanding, because of their good performance in environments with low signal-to-noise ratio. However, the computational complexity is one of their major disadvantages. In this paper a new method for detecting primary users is proposed using the modulation spectrum, which offers a good performance in environments with low signal to noise ratio and a low computational complexity. To prove that, a performance comparison is done, considering a DS-CDMA scheme, between the based-spectral correlation algorithm and the proposed in this work.