  Higher-order topological insulators (HOTIs) have attracted much attention in
photonics due to the tightly localized disorder-robust corner and hinge states.
Here, we reveal an unconventional HOTI phase with vanishing dipole and
quadrupole polarizations. This phase arises in the array of evanescently
coupled waveguides hosting degenerate $s$- and $d$-type orbital modes arranged
in a square lattice with four waveguides in the unit cell. As we prove, the
degeneracy of the modes with the different symmetry gives rise to the
nontrivial topological properties rendering the system equivalent to the two
copies of anisotropic two-dimensional Su-Schrieffer-Heeger model rotated by
90$^\circ$ with respect to each other and based on $s\pm d$ hybridized
orbitals. Our results introduce a route to tailor higher-order band topology
leveraging both crystalline symmetries and accidental degeneracies of the
different orbital modes.
