  Lagrangian of a classical conformal Yang-Mills field in the flat space of
even dimension greater than or equal to six involves higher derivatives. We
study Lagrangian formulation of the classical conformal Yang-Mills field by
using ordinary-derivative (second-derivative) approach. In the framework of the
ordinary-derivative approach, a field content, in addition to generic
Yang-Mills field, consists of auxiliary vector fields and Stueckelberg scalar
fields. For such field content, we obtain a gauge invariant Lagrangian with the
conventional second-derivative kinetic terms and the corresponding gauge
transformations. The Lagrangian is built in terms of non-abelian field
strengths. Structure of a gauge algebra entering gauge symmetries of the
conformal Yang-Mills field is described. FFF-vertex of the conformal Yang-Mills
field which involves three derivatives is also obtained. For six, eight, and
ten dimensions, eliminating the auxiliary vector fields and gauging away the
Stueckelberg scalar fields, we obtain a higher-derivative Lagrangian of the
conformal Yang-Mills field. For arbitrary dimensions, we demonstrate that all
auxiliary fields can be integrated out at non-linear level leading just to a
local higher-derivative action which is expressed only in terms of the generic
Yang-Mills field.
