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In this letter, a new blind sensing method based on the Cholesky factorization of the sample covariance matrix is presented for cognitive radios (CR). The proposed method overcomes the noise uncertainty problem of the energy detector (ED) and can also perform well without information about the channel, the primary signal and the noise power. Most importantly, unlike other detectors based on the sample covariance matrix (including the covariance absolute value (CAV), the maximum-minimum eigenvalue (MME), and the maximum eigenvalue trace (MET) detectors), the decision threshold for the proposed detector can be determined using an exact non-asymptotic expression without any asymptotic assumptions on the sample size and the sample dimension. Numerical simulations show the superiority of the new detector to the CAV, MME and MET detectors.