  We study quasi-quadratic modules in a pseudo-valuation domain $A$ whose
strict units admit a square root. Let $\mathfrak X_R^N$ denote the set of
quasi-quadratic modules in an $R$-module $N$, where $R$ is a commutative ring.
It is known that there exists a unique overring $B$ of $A$ such that $B$ is a
valuation ring with the valuation group $(G,\leq)$ and the maximal ideal of $B$
coincides with that of $A$. Let $F$ be the residue field of $B$. In the above
setting, we found a one-to-one correspondence between $\mathfrak X_A^A$ and a
subset of $\prod_{g \in G,g \geq e} \mathfrak X_{F_0}^F$.
