MD-80 TCASII RA HAD LTSS FROM ACR X. SYS ERROR. EVASIVE ACTION TAKEN.

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AN AIR TAXI TO SF34 DEPARTED THE ARPT HDG 280 DEGS. ABOUT 5 MI W OF THE ARPT; I TURNED THE ACFT TO 315 DEGS TO GAIN THE REQUIRED IN-TRAIL SEPARATION WITH A PRECEDING DEP. 2 DEPS LATER; AN MD-80 DEPARTED THE SAME RWY HDG 260 DEGS; AS REQUIRED FOR NOISE ABATEMENT. WHEN THE MD-80 WAS OUT OF 3600 FT MSL; I TURNED TO HIM TO 320 DEGS; WHICH WAS ABOUT ON-COURSE. WHEN THE MD-80 WAS ABOUT 5-6 MI BEHIND THE SF34; WITH BOTH CLBING OUT; I TURNED THE SF34 L TO 245 DEGS TO INTERCEPT HIS ON-COURSE; EXPECTING THIS TO PROVIDE DIVERGING-COURSE SEPARATION FROM THE MD-80; WHICH WAS OVERTAKING THE SF34 BY ABOUT 100 KTS. WHEN THE ACFT WERE ABOUT 4 MI APART; I ISSUED TFC TO THE MD-80; AND HE RESPONDED INSIGHT. 2 XMISSIONS LATER; I ISSUED TFC TO THE SF34 AS PASSING BEHIND AND TO YOUR L. HE ALSO RESPONDED IN SIGHT AND THAT HE HAD RECEIVED AN RA FROM HIS TCASII. AT THIS POINT; THE MD-80 QUESTIONED THE OP ADVISING THE SF34 HAD BEEN RIGHT IN FRONT OF HIM AND HE RESPONDED TO A DSCNT RA FROM HIS TCASII IN ORDER TO AVOID A CONFLICT. ALL THE WHILE; I FELT THAT WHILE THE ACFT DID GET CLOSER THAN I ANTICIPATED; I HAD LEGALLY SEPARATED THEM WITH COURSE DIVERGENCE. AFTER BEING ADVISED BY THE MD-80'S COMPANY OF THE CAPT'S DESIRE TO FILE A NMAC RPT; WE GENERATED A COMPUTER PLOT OF THE 2 ACFT'S RELATIVE POS DURING THE OP. IT WAS AT THIS TIME I FOUND THAT; WHEN I THOUGHT THE 2 ACFT WERE DIRECTLY IN-TRAIL AND I WAS TURNING THE SF34 OUT OF THE WAY OF THE MD-80; THE SF34 WAS; IN REALITY; SLIGHTLY TO THE R OF THE MD-80; SUCH THAT WHEN I TURNED HIM L; I HAD ACTUALLY TURNED HIM INTO THE MD-80'S PATH INSTEAD OF AWAY FROM IT. THE NEAREST PROX PRIOR TO DIVERGENCE WAS ABOUT 500 FT AND 1.8 MI.