Let $m imes n$ denote the set of all $m imes n$ matrices over a semiring $S$. For $Ain m imes n$, {it zero-term rank} of $A$ is the minimal number of lines (rows or columns) needed to cover all zero entries in $A$. In cite{BSL}, the authors obtained that a linear operator on $m imes n$ preserves zero-term rank if and only if it preserves zero-term ranks $0$ and $1$. In this paper, we obtain new characterizations of linear operators on $m imes n$ that preserve zero-term rank. Consequently we obtain that a linear operator on $m imes n$ preserves zero-term rank if and only if it preserves two consecutive zero-term ranks $k$ and $k+1$, where $0le kle min{m,n}-1$ if and only if it strongly preserves zero-term rank $h$, where $1le h le min{m,n}$.

Keywords: Semiring, zero-term rank, linear operator, (strongly) preserve