In this paper we describe a falls detection and classification algorithm for discriminating falls fromdaily life activities using a MEMS accelerometer. The algorithm is based on a shallow Neural Networkwith three hidden layers, used as fall/non fally classifier, trained with daily life activities features andfall features. The novelty of this algorithm is that synthetic falls are generated as multivariate randomGaussian features, so only real daily life features must be collected during some day of normal living.Moreover, the features related to synthetic fall events are generated as complement of normal features.First of all, the features acquired during daily life are clustered by Principal Component Analysis andno Fall activities shall be recorded. The complement set of the normal features is found and used as amask for Monte Carlo generation of synthetic fall. The two feature sets, namely the features recordedfrom daily life activities and those artificially generated are used to train the Neural Network. Thisapproach is suitable for a practical utilization of a Neural Network based fall detection characterizedby high Recall-Precision rate.