In this paper, an approach to recursive subspace identification based on the coordinate-free framework of subspace identification is proposed. Herein, the predictor space serves as a natural basis for the formulation of a recursive approach. Compressing the necessary past information, the predictor space of a previous identification will be used for subsequent identifications. Implementational difficulties, which all recursive methods are faced with and hampering an accurate tracking of fast changes of the system, are also addressed.