The two aircraft, a Beech U-21A and a Piper PA-31-350, collided nearly head on at 7,000 ft MSL over Independence, MO. The collision occurred in daylight VMC conditions with a visibility of 20 miles. The U-21 was in level cruise and the PA-31 was climbing eastbound to an undisclosed altitude enroute to Saint Louis. Both aircraft were equipped with operating Mode-C transponders but the controller in contact with the U-21 did not observe the conflict and traffic advisories were not provided. The PA-31 was operating in accordance with visual flight rules. The U-21 was operating in accordance with instrument flight rules. After the collision, both aircraft crashed in uncontrolled descent. There was no indication that either aircraft took any evasive action. The conflict alert subprogram of the ARTS III tracking system was not programmed to alert the controllers to the impending collision and the two controllers did not observe any target in the vicinity of the data block representing the U-21. (See NTSB/AAR-88/01).