  Using generalized field strength tensors for non-Abelian tensor gauge fields
one can explicitly construct all possible Lorentz invariant quadratic forms for
rank-4 non-Abelian tensor gauge fields and demonstrate that there exist only
two linear combinations of them which form a gauge invariant Lagrangian.
Together with the previous construction of independent gauge invariant forms
for rank-2 and rank-3 tensor gauge fields this construction proves the
uniqueness of early proposed general Lagrangian up to rank-4 tensor fields.
Expression for the coefficients of the general Lagrangian is presented in a
compact form.
