  Let $\pi:sl(n|n)\to A(n-1,n-1)$ be the natural epimorphism of Lie
superalgebra. Then $\dim\ker\pi=1$. Let $\pi^{(t)}:sl^{(t)}(n|n)\to
A^{(t)}(n-1,n-1)$ be the natural epimorphism, where $t=1,2,4$. Let
$\{e_k|k\in{\mathbb{Z}}\}$ be the basis of $\ker\pi^{(t)}$ with $e_k\in
sl^{(t)}(n|n)_{(a_tk+b_t)\delta}$, where $(a_1,b_1)=(1,0)$, $(a_2,b_2)=(2,-1)$
and $(a_4,b_4)=(4,-2)$. The main result of this paper is to explicitly describe
an element of $U_q(sl^{(t)}(n|n))$ (and its multi-parameter version)
corresponding to $e_1$ (i.e., $k=1$). As for $U_q(sl^{(1)}(n|n))$ (i.e.,
$t=1$), the author had already had explicit description for every $k$ in 1999.
