Observer design is one of large fields investigated in automatic control theory and a lot of articles have already been dedicated to it in technical literature. Non-linear observer design method based on dissipation normal form proposed in the paper represents a new approach to solving the observer design problem for a certain class of non-linear systems. As the theoretical basis of the approach the well known dissipative system theory has been chosen. The main achievement of the contribution consists in the fact that the error dynamics of the observer is priory chosen non-linear. It provides more flexibility in the sense of specifying error convergence properties to zero in comparison with other techniques. Lyapunov's stability theory is the other basic point of the approach.