A novel analysis of the chemical bonding pattern in the valence isoelectronic series of triatomic molecules O-3, S-3, SO2, and OS2 is reported It is based on examining the bond order matrix elements between the oriented localized molecular orbitals (OLMOs) that are localized on the three individual atoms. left (L), center (C), and right (R) The analysis indicates that there is a (L-C) and (C-R) pi-bonding interaction and a (L-R) pi-antibonding interaction. It supports the earlier proposed "partial biradical" interpretation of these systems, which had recently been challenged The degree of biradical character is shown to increase from SO2 to S-3 to O-3 to OS2.