In this paper, global adaptive output feedback tracking problem is considered for a class of multivariable nonlinear systems with unknown parameters and nonlinear terms linear in unmeasured states. Based on a modified high-gain observer and symmetric positive diagonal unity upper triangular factorisation of high-frequency gain matrix, an adaptive backstepping design is proposed, which is able to guarantee global stability of the closed-loop system and circumvent the over-parameterisation problem raised by using conventional backstepping method. Moreover, with the introduction of an error modification and an initialisation technique, it is proved that the tracking performance can be achieved.