A connector has means for preventing terminal fittings from being inserted in an inverted manner, and in which nothing protrudes from outer faces of these terminal fittings. Cut-away portions 17 are formed at a ceiling side of anterior ends of left and right side plates 11B of a box-shaped member 11 of a terminal fitting 10. Protrusions 34 are formed within a cavity 24 at anterior ends of left and right wall faces thereof, in locations somewhat removed from a wall face having a lance 26 formed thereon. These protrusions 34 are capable of fitting into the cut-away portions 17. When the terminal fitting 10 is correctly inserted, the protrusions 34 fit into the cut-away portions 17, and the terminal fitting 10 is pushed into a correct position and is retained by the lance 26. When the terminal fitting 10 is inserted in an inverted manner, the anterior end of the box-shaped member 11 strikes against the protrusions 34 before the terminal fitting 10 reaches the correct position. Consequently, the terminal fitting 10 is prevented from being inserted any further, and it is not retained by the lance 26.