A connector is provided with a first fastening member 55 having an engagement hole 53 freely engaging with a head portion of an implant 41 screwed and inserted to a body of vertebra and a fastening groove 57, a second fastening member 63 having an insertion hole 61 freely inserting a rod 49 therethrough and a fastening groove 65, and a fastening device 69 freely penetrating a through hole 59 crossing to the fastening groove 57 in the first fastening member 55 and a through hole 67 crossing to the fastening groove 65 in the second fastening member 63, and an angle adjusting and engaging portion is provided on connecting surfaces 55a and 63a between the first fastening member 55 and the second fastening member 63.