  Since the first exposition of the complex Frobenius structures (\cite{N}),
there have been considerable development and many new applications on this
subject(see \cite{G}, \cite{H1},\cite{HT}, \cite{S}, \cite{Web},\cite{W} and
references therein). Inspired by complex Frobenius structures, L. H{\"o}rmander
introduced a class of first order overdetermined systems of partial
differential equations (\cite{H1}) and established existence theorems. This
paper is devoted to the construction of resolution for the solution sheaves of
these overdetermined systems considered in \cite{H1}. A sufficient condition
for global exactness is obtained, which leads to gluing technique for local
solutions of the overdetermined systems by solving Cousin type problems. In
addition, we also prove local solvability of the Treves complex without
assuming the non-degeneracy of the Levi form.
