In this paper we will use the theory of differential subordinations to obtain a new condition for meromorphic functions, defined in the punctured disc $\dot U=U\backslash\{0\}$, $U=\{z\in\mathbb C:|z|<1\}$, which are of the form $f(z)=\frac1z+a_nz_n+a_{n+1}z^{n+1}+\ldots$, to be starlike functions. The new condition for starlikeness is expressed by means of $|(1-\alpha)zf(z)+z^2f'(z)+\alpha|$, where $\alpha\in[0,1)$.