Corrigendum to “A New Algorithm for Gröbner Bases Conversion” [J. Symb. Comput. 128 (2025) 102391]

In (Hashemi and Kapur, 2025), we proposed an algorithm for converting a given Gröbner basis into a Gröbner basis with respect to another term ordering. A recent counterexample due to Heisel and Lauritzen (2025) shows that the presented algorithm is not correct as stated. In this short note, we identify the precise source of the failure, propose a corrected variant of the algorithm and prove that it returns, in finitely many steps, a Gröbner basis with respect to the target term ordering.