  In recent lattice calculations it has been discovered that mesons upon
truncation of the quasi-zero modes of the Dirac operator obey a symmetry larger
than the $SU(2)_L \times SU(2)_R\times U(1)_A$ symmetry of the QCD Lagrangian.
This symmetry has been suggested to be $SU(4) \supset SU(2)_L \times
SU(2)_R\times U(1)_A$ that mixes not only the u- and d-quarks of a given
chirality, but also the left- and right-handed components. Here it is
demonstrated that bilinear $\overline{q}q$ interpolating fields of a given spin
$J \geq 1$ transform into each other according to irreducible representations
of $SU(4)$ or, in general, $SU(2N_F)$. This fact together with the coincidence
of the correlation functions establishes $SU(4)$ as a symmetry of the $J \geq
1$ mesons upon quasi-zero mode reduction. It is shown that this symmetry is a
symmetry of the confining instantaneous charge-charge interaction in QCD.
Different subgroups of $SU(4)$ as well as the $SU(4)$ algebra are explored.
