  We introduce a variant of dipole representation for composite fermions in a
half-filled Landau level, taking into account the symmetry under exchange of
particles and holes. This is implemented by a special constraint on composite
fermion and composite hole degree of freedom (of an enlarged space), that makes
the resulting composite particle, dipole, a symmetric object. We study an
effective Hamiltonian, that commutes with the constraint on the physical space,
and fulfills the requirement for boost invariance on the Fermi level. The
calculated Fermi liquid parameter F2 is in a good agreement with numerical
investigations in [Phys. Rev. Lett. 121, 147601 (2018)].
