  We study a higher derivative (HD) field theory with an arbitrary order of
derivative for a real scalar field. The degree of freedom for the HD field can
be converted to multiple fields with canonical kinetic terms up to the overall
sign. The Lagrangian describing the dynamics of the multiple fields is known as
the Lee-Wick (LW) form. The first step to obtain the LW form for a given HD
Lagrangian is to find an auxiliary field (AF) Lagrangian which is equivalent to
the original HD Lagrangian up to the quantum level. Till now, the AF Lagrangian
has been studied only for N=2 and 3 cases, where $N$ is the number of poles of
the two-point function of the HD scalar field. We construct the AF Lagrangian
for arbitrary $N$. By the linear combinations of AF fields, we also obtain the
corresponding LW form. We find the explicit mapping matrices among the HD
fields, the AF fields, and the LW fields. As an exercise of our construction,
we calculate the relations among parameters and mapping matrices for $N=2,3$,
and 4 cases.
