  In this paper, we consider a new type of urn scheme, where the selection
probabilities are proportional to a weight function, which is linear but
decreasing in the proportion of existing colours. We refer to it as the
\emph{negatively reinforced} urn scheme. We establish almost sure limit of the
random configuration for any \emph{balanced} replacement matrix $R$. In
particular, we show that the limiting configuration is uniform on the set of
colours, if and only if, $R$ is a \emph{doubly stochastic} matrix. We further
establish almost sure limit of the vector of colour counts and prove central
limit theorems for the random configuration, as well as, for the colour counts.
