Some criteria for determining the normality of the family $F$ of meromorphic functions in the unit disc, which share values depending on $fin F$ with their derivatives is obtained. The new results in this paper improve some earlier related results given by Pang and Zalcman cite{Pang}, Fang and Zalcman cite{Fang}, A. P. Singh and A. Singh cite{A.Singh}.

Keywords: meromorphic function, shared value, normal family