In this talk, we present a basis-preserving algorithm for computing the approximate greatest common divisor of several univariate Newton polynomials. The method avoids the numerical instability introduced by converting polynomials to monomial basis, as it directly operates within Newton basis. By extending Barnett's theorem via Bezout matrices to Newton polynomials, the algorithm preserves the input basis for both the polynomials and the output AGCD. Illustrative examples are provided to demonstrate the superior numerical stability of the proposed method compared to the methods relying on basis transformation.