This paper presents an indirect adaptive control scheme for linear Systems which may possibly be a nonminimum phase. The control scheme achieves asymptotical pole placement without either introducing persistent excitation probing signals into the systems or assuming any a priori knowledge on the plant parameters. The system order is the only a priori knowledge required on the plant. The adaptive control law is free from singularities in the sense that the estimated plant model is always controllable. The singularities are overcome by a suitable parameter estimates modification which is based upon standard least squares covariance matrix properties. The analysis of the stability and the global convergence of a closed-loop system is given in detail for both discrete-time and continuous-time systems.