Abstract: Let $\F$ be a family of meromorphic functions on a domain
$D$, $a$ and $b$ be two nonzero finite complex numbers($\frac{a}{b}$
not positive integer). If for every $f \in \F$, $f(z) = a
\Rightarrow f^{(k)}(z) = a$, and the zeros multiplicity of $f - a$
is at least $k$, and $|f(z) - a| \geq \varepsilon$ ($\varepsilon >
0)$ whenever $f^{(k)}(z) = b$, then $\F$ is normal on $D$.

Key words: meromorphic function, zero point, normality