When chemical plants exhibit linear behaviour in the range of the operating point, powerful multivariate statistical methods exist for fault detection. However, methods to handle non-linear processes are yet to reach the same stage of maturity and more efforts need to be directed towards finding effective methods to handle a wide class of non-linearities and facilitate easy on-line implementation. This work presents a novel method for on-line fault detection in non-linear systems using Self-Organizing Maps (SOM). SOM is a topology-preserving unsupervised neural network algorithm that projects high dimensional data onto a two-dimensional map. The detection procedure consists of training SOM with normal operating data followed by projections of new data onto the trained map. A new metric used for detection is the difference between the distance of the test point and the average distance of the members of the best matching unit with respect to the weight vector of that unit. A threshold value for the proposed metric that minimizes Type I and Type II errors is identified using Monte Carlo simulations. The efficacy of the proposed method is validated through simulation studies on non-linear systems, viz. i) CSTR and ii) Bio-reactor.