  Let $K$ be a complete discrete valued field with residue field $k$ and $F$
the function field of a curve over $K$. Let $A \in {}_2Br(F)$ be a central
simple algebra with an involution $\sigma$ of any kind and $F_0 =F^{\sigma}$.
Let $h$ be an hermitian space over $(A, \sigma)$ and $G = SU(A, \sigma, h)$ if
$\sigma$ is of first kind and $G = U(A, \sigma, h)$ if $\sigma$ is of second
kind. Suppose that $\text{char}(k) \neq 2$ and ind$(A)\leq 4$. Then we prove
that projective homogeneous spaces under $G$ over $F_0$ satisfy a local-global
principle for rational points with respect to discrete valuations of $F$.
