MIMO system identification is a fundamental concern in a variety of applications. Various iterative and recursive MIMO system identification algorithms exist in the literature. The iterative algorithms suffer from high computational cost due to large matrix computations and recursive algorithms suffer from slow convergence speed. This paper proposes a fast recursive exact least squares algorithm for MIMO system identification with fast convergence speed and low computational cost. The recursions of the algorithm give rise to a lattice structure. The lattice structure is less sensitive to round-off errors, coefficients variations and can also be used for model order reduction. Although in this work we estimate an FIR (finite impulse response) model of the MIMO system, the framework can also be used for IIR (infinite impulse response) models, and for estimating linear periodically time varying (LPTV) and multivariable systems. The theory proposed is validated using simulation results.