  \[H0\] Let $a$ be a nonzero complex value, let $n$ be a nonnegative integer, and $n_0,\dots,n_k,t_0,\dots,t_k$ be positive integers. Let $\mathcal F$ be a family of meromorphic functions in a complex domain $D$ such that for every $f\in\mathcal F,$ $f^n(f^{n_0})^{(t_0)}\cdots(f^{n_k})^{(t_k)}-a$ is nowhere vanishing on $D.$ Assume that  $a)$ $n_j\geq t_j \text{\;for all \;} 0\leqslant j\leqslant k,$  $b)$ $n+\sum_{j=0}^kn_j\geq 0+\sum_{j=0}^kt_j.$\ Then $\mathcal F$ is normal on $D.$  