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This letter proposes a new method for multiband radar signal fusion by making use of all-phase fast Fourier transform (apFFT) algorithm and iterative adaptive approach (IAA). Central to the proposed method are, first, the mutual incoherence compensation between various subbands by apFFT algorithm, and second, the application of IAA to the mutually coherent subband measurements for signal fusion. Taking advantage of both algorithms, the proposed method effectively improves the range resolution with low sidelobes and performs robustly in the presence of noise. In particular, it requires no model information and therefore enables flexible implementation for practical application. The feasibility and effectiveness of the proposed algorithm are validated through both numerical simulations and raw data processing results.