In this correspondence additional results on majority-logic decoding of product codes are presented. If one of the component codes is decodable using Rudolph\´s nonorthogonal algorithm, and the other using Reed-Massey\´s

-step orthogonalization, then the resulting product code is majority-logic decodable in

steps, where nonorthogonal checks are used in the first step and orthogonal checks in the remaining steps. If the component codes are both decodable using Rudolph\´s algorithm, the product code is majority-logic decodable using the same procedure.