  In this paper, we investigate the power functions $F(x)=x^d$ over the finite
field $\mathbb{F}_{2^{4n}}$, where $n$ is a positive integer and
$d=2^{3n}+2^{2n}+2^{n}-1$. It is proved that $F(x)=x^d$ is APcN at certain
$c$'s in $\mathbb{F}_{2^{4n}}$, and it is the second class of APcN power
functions over finite fields of even characteristic. Further, the
$c$-differential spectrum of these power functions is also determined.
