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The stable normalised least‐mean fourth (SNLMF) algorithm is developed in the passive bistatic radar (PBR) system to realise the interference cancellation. The larger power of the reference signal may lead to the poor convergence rate. By replacing the reference signal vector with the instantaneous echo signal, the concept of the clutter attenuation (CA) is introduced in the SNLMF algorithm, and the CA‐SNLMF algorithm is proposed to provide a fast convergence. The real measured data collected from the PBR system demonstrate that the proposed CA‐SNLMF algorithm has a faster convergence speed and better cancellation performance than the SNLMF algorithm.