The continuity of the star-kernel of quasidifferentials of a quasidifferentiable function with a star-equivalent bounded quasidifferential sub-family are studied and parts of results are represented in this note. It also has been pointed out that the directional subderivative and superderivative of a function can be expressed as support functions of its star-kernel if the star-kernel can be generated by a quasidifferential of the function.