A vertically insertable-detachable connector which includes male and female connectors, and can be reduced in height to provide a compact construction when the two connectors are connected together, and can easily achieve waterproof and dust-prevention effects, and can save a space required for mounting a harness. The male connector include a male terminal having a wire retaining portion and a fitting contact tongue extending in a direction perpendicular to a direction of extension of a wire, and a housing containing the male terminal therein and having a notch which is formed at a front end portion thereof, the watch opening in a direction of extension of the fitting contact tongue. The female connector includes a female terminal having a wire retaining portion and a fitting hole extending in a direction perpendicular to a direction of extension of a wire, and a housing containing the female terminal therein and having a notch which is formed at a front end portion thereof, the notch opening in a direction of the opening of the fitting hole. When the fitting contact tongue is inserted and fitted in the fitting hole, the notched front end portions of the two connectors are connected together, thereby reducing a deviation of the two wires from each other in a direction perpendicular to the axes of the two wires.