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Noise attenuation plays an important role in interpreting potential fields. Some approaches to denoise potential field data are classical low-pass filters, upward continuation, and non-local means. We propose a noise removal approach based on upward continuation, but keeping the original survey altitude. For this purpose, we upward-continue the data and subsequently apply downward continuation to bring the data back to its original height of observation. Upward continuation is performed in the wavenumber domain and downward continuation is based on a high-order Taylor-series method. Ideally, the data would remain unchanged by these operations, but since the latter truncates the Taylor series expansion of the function, whose high order terms contain high frequency components, they yield a low-pass filter that proved to be highly effective for denoising the data without compromising accuracy. We demonstrate the proposed approximation for reducing the noise of archaeological magnetometric field data from northwest Slovakia.