Let $(\pi,V)$ be a generic irreducible representation of a general linear group over a $p$-adic field. Jacquet, Piatetski-Shapiro, and Shalika gave an open compact subgroup $K$, so that the subspace $V^{K}$ consisting of $v \in V$ fixed by $K$ is one-dimensional. If $\pi$ has a Shalika model $¥Lambda$, then we call vectors in $\Lambda(V)$ the Shalika forms of $\pi$, and those in $\Lambda(V^{K})$ the Shalika newforms. In this article, in the case where $\pi$ is supercuspidal, we show the nonvanishing of Shalika newforms at a minimal point in a sense. This point is not the identity, and the Shalika newform vanishes at the identity, if the character defining the Shalika model is ramified. In view of this result, in this case, we give another Shalika form with nice properties. This study was undertaken to demonstrate that the L- and epsilon- factors in Gan-Takeda's local Langlands correspondence for GSp(4) appear in the newform for GSp(4) (not only for $PGSp_4$ by Roberts-Schmidt).