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Noise term in the reconstruction matrix in ghost imaging is a major cause of blurring imaging results. To remedy this problem, we propose a new ghost imaging method based on the binomial theorem to reduce the level of noise. In our method, images with low-level noise can be generated by constructing a binomial formula using high-order imaging results that are acquired by reintroducing the reconstruction result back into the imaging formula repeatedly. Experimental and simulation results demonstrate that our method is effective in improving imaging quality and the anti-interference performance and reducing computing time, making it useful for practical applications.