Checkerboard-like　markers　are　widely　applied　in　visual　localization　applications,　including　SLAM,　augmented　reality,　robot　navigation,　and　3-D　scene　reconstruction.　Most　corner　detectors　assume　that　the　marker　is　attached　to　a　flat　surface,　which　severely　limits　the　placement　of　the　marker　and　thus　reduces　the　scope　of　use　for　these　applications.　However,　in　some　scenarios,　it　is　not　easy　to　find　an　ideal　flat　surface　required　by　most　corner　detectors　in　a　given　scenario,　in　which　case　the　marker　can　often　only　be　fixed　on　a　curved　surface.　Therefore,　the　accuracy　of　most　corner　detectors　may　be　reduced.　In　this　study,　a　novel　method　is　proposed　with　subpixel　accuracy　to　detect　and　locate　the　corners　on　a　chessboard-like　marker,　which　is　either　flat　or　curved.　The　proposed　method　fits　multisegment　curves　in　a　quadratic　form　to　the　edges　in　a　checkerboard-like　marker.　The　exact　corner　positions　are　considered　as　the　intersections　of　the　corresponding　curves　with　analytical　solutions.　The　proposed　method　achieves　the　state-of-the-art　performance　through　experiments,　including　synthetic　corner　localization　test,　real-world　stereo　vision　triangulation　experiment,　and　pose　estimation　on　a　curved　object,　demonstrating　the　superiority　of　our　method.