  We introduce the concept of the locally unextendible non-maximally entangled
basis (LUNMEB) in $H^d \bigotimes H^d$. It is shown that such a basis consists
of $d$ orthogonal vectors for a non-maximally entangled state. However, there
can be a maximum of $(d-1)^2$ orthogonal vectors for non-maximally entangled
state if it is maximally entangled in $(d-1)$ dimensional subspace. Such a
basis plays an important role in determining the number of classical bits that
one can send in a superdense coding protocol using a non-maximally entangled
state as a resource. By constructing appropriate POVM operators, we find that
the number of classical bits one can transmit using a non-maximally entangled
state as a resource is $(1+p_0\frac{d}{d-1})\log d$, where $p_0$ is the
smallest Schmidt coefficient. However, when the state is maximally entangled in
its subspace then one can send up to $2\log (d-1) $ bits. We also find that for
$d= 3$, former may be more suitable for the superdense coding.
