  We consider weighted negatively reinforced urn schemes with finitely many
colours. An urn scheme is called negatively reinforced, if the selection
probability for a colour is proportional to the weight $w$ of the colour
proportion, where $w$ is a non-increasing function. Under certain assumptions
on the replacement matrix $R$ and weight function $w$, such as, $w$ is
differentiable and $w(0) < \infty$, we obtain almost sure convergence of the
random configuration of the urn model. In particular, we show that if $R$ is
doubly stochastic the random configuration of the urn converges to the uniform
vector, and asymptotic normality holds, if the number of colours in the urn are
sufficiently large.
