  We give a simple technic to derive the Berry-Ess\'een bounds for the
quadratic variation of the subfractional Brownian motion (subfBm). Our approach
has two main ingredients: ($i$) bounding from above the covariance of quadratic
variation of subfBm by the covariance of the quadratic variation of fractional
Brownian motion (fBm); and ($ii$) using the existing results on fBm in
\cite{BN08,NP09,N12}. As a result, we obtain simple and direct proof to derive
the rate of convergence of quadratic variation of subfBm. In addition, we also
improve this rate of convergence to meet the one of fractional Brownian motion
in \cite{N12}.
