The paper deals with the transformation of linear single-input/single-output (SISO) systems into Frobenius canonical form of which the ultimate objective is to achieve a new and computationally efficient methodology towards a desired pole placement. The classical formula of Ackermann is generalised for both time-invariant and time-varying systems as a result of this study. The advantage of the proposed technique is that it does not require the computation of characteristic polynomial coefficients or the eigenvalues of the original system, nor the coefficients of the characteristic polynomial of the transformed system. Its computational efficiency is demonstrated to be superior in comparison with some other commonly used techniques.