• Quadratus F. Thiergart & U. Frantz, 1962 † (uncertain) [Phylum: Sporae dispersae]
• Quadratus Wisner, 1999 accepted as Eptatretus Cloquet, 1819 [Phylum: Chordata]
• Quadratus ancon Mok, Saavedra-Diaz & Acero P., 2001 accepted as Paramyxine ancon (Mok, Saavedra-Diaz & Acero P., 2001)
• Quadratus nelsoni (Kuo, Huang & Mok, 1994) accepted as Paramyxine nelsoni Kuo, Huang & Mok, 1994
• Quadratus taiwanae (Shen & Tao, 1975) accepted as Paramyxine taiwanae Shen & Tao, 1975
• Quadratus yangi (Teng, 1958) accepted as Paramyxine yangi Teng, 1958