A recursive identification algorithm for multivariable systems is developed by extending the SISO augmented UD identification (AUDI) algorithm developed by Niu, Fisher and Xiao in 1992. This least-squares type algorithm has a simple, compact structure and provides simultaneous identification of model structure and parameters, with excellent numerical properties. A multivariable input/output difference equation model is used as the model representation for identification, and it is shown how the corresponding (unique) canonical state-space representation can also be generated by a straightforward transformation. The algorithm is easier to interpret and more straightforward to implement than the corresponding RLS approaches.