It has been proven that there exists a one-to-one correspondence H(t, x) between solutions of the linear system and the nonlinear system in the previous work. However, there is no paper considering the Hölder regularity of the transformation H(t, x) in the literature. This paper fills the gap. We establish a strict proof of the Hölder regularity of the transformation H(t, x). We show that the conjugating function H(t, x) in the generalized Hartman–Grobman theorem is always Hölder continuous.