This paper proposes an innovative identification scheme to estimate parameters constituting linear relations in time-invariant systems: the bounding box recursive Frisch scheme. A novel recursive version of the Frisch scheme, a linear estimator characterised by mild prior assumptions in the error-in-variables (EIV) framework, has been derived. The fast computational time and convergence in the identification of linear systems are the most relevant feature of this recursive version of the scheme. The performance of the developed algorithm has been evaluated trough numerical simulations. Results proved the effectiveness and accuracy of the proposed solution.