  The study of `structure' on subsets of abelian groups, with small `doubling
constant', has been well studied in the last fifty years, from the time Freiman
initiated the subject. In \cite{DF} Deshouillers and Freiman establish a
structure theorem for subsets of $\n$ with small doubling constant. In the
current article we provide an alternate proof of one of the main theorem of
\cite{DF}. Also our proof leads to slight improvement of the theorems in
\cite{DF}.
