A non-linear canonical form observer design approach for multi-input multi-output systems x =f(x, u), y = h(x, u). with linearizable error dynamics is proposed in the paper, The method involves a transformation of the original non-linear system in a reduced generalized observer canonical form (RGOCF) by a non-linear state transformation, The name reduced comes from the fact that this non-linear canonical form has a reduced dependency on derivatives of the inputs. Necessary and sufficient conditions for transformability are derived and a transformation algorithm based on those conditions is developed. The non-linear observer is firstly designed in the canonical coordinates of the RGOCF and then it is presented in the original and observability coordinates. A final example including simulation is given for illustration.