In this paper, a new modular design technique for globally and practically adaptive output tracking of high-order lower-triangular nonlinear systems is proposed. This technique is not based on certainty equivalence principle and completely uses feedback domination method for these linearly parameterized systems. Contrary to the methods based on adding a power integrator technique, for adaptive control of high-order lower-triangular nonlinear systems, in which the choice of a parameter update law is limited to a Lyapunov-type algorithm, the present method does not have this restriction and uses the swapping identifier as its parameter update law. The modularity of designing the controller and the identifier in this method, which relies on control design using feedback domination approach, is completely different from modular design in Immersion and invariance (I&I) based method, which relies on identifier design and desired features of parameter identification. Finally an example illustrates the feasibility and efficiency of the proposed method.