  Let $M$ be a type I von Neumann algebra with the center $Z,$ a faithful
normal semi-finite trace $\tau.$ Let $L(M, \tau)$ be the algebra of all
$\tau$-measurable operators affiliated with $M$ and let $S_0(M, \tau)$ be the
subalgebra in $L(M, \tau)$ consisting of all operators $x$ such that given any
$\epsilon>0$ there is a projection $p\in\mathcal{P}(M)$ with
$\tau(p^{\perp})<\infty, xp\in M$ and $\|xp\|<\epsilon.$ We prove that any
$Z$-linear derivation of $S_0(M, \tau)$ is spatial and generated by an element
from $L(M, \tau).$
