  In this note we show that for the construction of differentiable conjugation,
the assumption of the existence of smooth bump function is not necessary, and
consequently the corresponding conjecture stated in the paper of W. Zhang, K.
Lu and W. Zhang "Differentiability of the Conjugacy in the Hartman-Grobman
Theorem" (\cite{ZLZ}) is incorrect. We show that instead of bump functions we
can use smooth blid maps. We also propose a construction of the blid map for
the space $X=C^0[0,1]$, which does not possess a smooth bump function.
