This note presents a robust direct adaptive control scheme with a new normalization technique and its stability analysis in the presence of unmodeled dynamics and/or bounded disturbances. Following input-output stability theory, L(2) and L infinity stability of the system is studied using the sector stability and passivity theorems and conditions for global stability are derived. It is also shown that robustness of the adaptive control system can be improved when relative dead zone and the novel normalization technique are incorporated into the scheme.