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We investigated the corner-states characteristics of C _4 -symmetric higher-order topological crystalline insulators. By evaluating the charge polarization and fractional corner charge, we obtained the abundant topological properties for different intercell hoppings amplitudes and identified that the non-trivial fractional corner charges are accompanied by second-order topological corner states. Interestingly, there are two different types of corner states topologically protected by generalized chiral symmetry, which guarantees that both corner states are pinned to zero energy. One of the corner states is localized at the corners like the one protected by generalized chiral symmetry of three-atom sublattice. However, the other corner states are localized at the two sublattices nearest to the corners, which has no counterpart in a lattice with generalized chiral symmetry. Moreover, both of them have robustness against defects and disorder.