  In this paper we extend to finite-dimensional Pontryagin spaces the methods
used in \cite{CasazzaLeon,Deguang} to build frames from an adjoint and positive
operator. It is proved that any frame in finite dimensional Pontryagin space
$\mathcal{K}$ is $J$-orthogonal projection of a frame for a space $\mathcal{H}$
such that $\mathcal{K}\subset\mathcal{H}$. Furthermore, given
$\{k_{n}\}_{n=1}^{m}$ and $\{x_{n}\}_{n=1}^{k}$ frames for $\mathcal{K}$ and
$\mathcal{H}$ respectively, we build a finite-dimensional Pontryagin space
$\mathfrak{K}$ and a frame $\{y_{n}\}_{n=1}^{N}$ for $\mathfrak{K}$ such that
$\mathcal{K},\mathcal{H}\subset\mathfrak{K}$ and
$\{k_{n}\}_{n=1}^{m},\{x_{n}\}_{n=1}^{k}\subset \{y_{n}\}_{n=1}^{N}$.
