In 1989, Kurosawa proposed a key changeable ID-based cryptosystem and a corresponding signature scheme. In Kurosawa's scheme, the legal users can change their public parameters by themselves without the help from a trusted third party. However, Kurosawa's digital signature scheme is insecure and impractical. The purpose of this paper is to point out the described problems and then to suggest a simple remedy, which will enable the modified ID-based digital signature to be more secure and practical.