Scanning-tunneling microscopy has been used to investigate the oxygen-induced c(2\ifmmode\times\else\texttimes\fi{}2n) (n=3, 4, and 5) structures on Rh(110). The results show that oxygen induces a (1\ifmmode\times\else\texttimes\fi{}n) reconstruction of the Rh substrate with every nth close-packed row along the [11\ifmmode\bar\else\textasciimacron\fi{}0] direction missing. This is in contrast to other oxygen-induced reconstructions of face-centered-cubic (110) surfaces where [001] rows are missing, and implies a different driving mechanism for the present case. On the basis of the images and the symmetry of the diffraction patterns, structural models are proposed.