For the reconstruction of the feedback polynomial of a synchronous scrambler placed after a convolutional encoder, the existing algorithms require the prior knowledge of a dual word of the convolutional code. To address the case of a dual word being unknown, a new algorithm for the reconstruction of the feedback polynomial based on triple correlation characteristic of an m-sequence is proposed. First, the scrambled convolutional code sequence is divided into bit blocks; the product of the scrambled bit blocks with a dual word is proven to be an m-sequence with the same period as the synchronous scrambler. Second, based on the triple correlation characteristic of the generated m-sequence, a dual word is estimated; the generator polynomial of the generated m-sequence is computed by two locations of the triple correlation peaks. Finally, the feedback polynomial is reconstructed using the generator polynomial of the generated m-sequence. As the received sequence may contain bit errors, a method for detecting triple correlation peaks based on the constant false-alarm criterion is elaborated. Experimental results show that the proposed algorithm is effective. Ulike the existing algorithms available, there is no need to know a dual word a priori and the reconstruction result is more accurate. Moreover, the proposed algorithm is robust to bit errors.