  In 1960, D.G. Northcott proved that if $e_0(I)$ and $e_1(I)$ denote zeroth
and first Hilbert-Samuel coefficients of an $\mathfrak m$-primary ideal $I$ in
a Cohen-Macaulay local ring $(R,\mathfrak m)$, then $e_0(I)-e_1(I)\le \ell
(R/I)$. In this article, we study an analogue of this inequality for
Buchsbaum-Rim coefficients. We prove that if $(R,\mathfrak m)$ is a two
dimensional Cohen-Macaulay local ring and $M$ is a finitely generated
$R$-module contained in a free module $F$ with finite co-length, then
$br_0(M)-br_1(M)\le \ell (F/M)$, where $br_0(M)$ and $br_1(M$) denote zeroth
and first Buchsbaum-Rim coefficients respectively.
