In this study, the authors propose a neural network (NN) method that uses feature points and the angles formed between the points to recognise facial expressions. Accurate facial expression recognition is an important part of affective computing with many practical applications. Yet, achieving acceptable levels of facial recognition accuracy has proven difficult. Feature points and the distances between the points are used to model basic expressions in NN-based approaches, but, in some cases, they cannot generate satisfactory performance. They expand on the characterisation of facial expression by considering the angles formed between feature points to augment the amount of information that is sent to the NNs. Furthermore, to circumvent a common challenge in facial expressions recognition, which is the difficulty of differentiating among several expressions, they designed a post-processing step to assess the output of the NN against a threshold. The whole method makes a decision only when the output of the NN exceeds the threshold. Otherwise, the frame under consideration is assigned to a ‘no decision’ class. They tested our method on the widely used facial expression CK + database and found that it can achieve good accuracy.