To fit male and female connector housings together without tilting, an inner bottom surface of a hood portion of a male connector housing has step portions formed at the four respective corner portions, and a recessed portion having a lower height than the step portions. The female connector housing can be fully inserted because of a gap provided between a bulged portion of the female connector housing and the recessed portion. The female connector housing, when further inserted, slides at its opposite ends to change its posture so that male and female terminals are completely connected together.