The problem of non-overshooting output tracking of feedback linearisable single-input-single-output nonlinear systems is considered. We present a controller design procedure which makes use of feedback linearisation and global coordinate transformation techniques and is applicable to the cases with a variety of reference inputs and possibly non-zero initial conditions. For systems with low relative order, the sets of feasible controller parameters are constructed and the presented conditions for determining these sets are sufficient and necessary. For systems with higher relative order, an approach to construct such sets is proposed where the conditions are sufficient. Two illustrative examples are provided to show the effectiveness of the results.