EMB135 FO REPORTS STRANGE FMC MALFUNCTION DURING ARGAL ARRIVAL TO RDU CAUSING TRACK DEV.

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SHORTLY AFTER PASSING OVER HPW FIX; THE FMS STARTED ON THE ARGAL 5 ARR; THEN PROCEEDED DIRECTLY TO RDU. AFTER ATC QUERIED; WE TOOK A HDG; GOT BACK ON COURSE; NO ISSUES OR CONFLICTS STATED BY ATC. THE FMS DROPPED THE ARR ON THE MFD; BUT KEPT IT IN THE BOX. AFTER GOING DIRECTLY TO FIX; THE FMS DREW A STRANGE COURSE PAST THE MISSED APCH; AND ONTO A RANDOM FIX OVER 100 NM AWAY. WE BOTH LOOKED BEWILDERED ALONG WITH ANOTHER CAPT IN THE JUMPSEAT. AFTER DELETING THE RANDOM FIX INTO THE FUTURE; THE PF (CAPT) THEN DREW A NORMAL COURSE ON THE MFD. AT THIS TIME; I COULD NOT BELIEVE MY EYES AS; HE CLRED OUT HIS FMS WITH THE RANDOM FIX; MY MFD DREW THE SAME COURSE OUT OF NOWHERE. I NOW HAD A STRANGE COURSE ON MY MFD; I QUICKLY DELETED THE STRANGE FIX; AND WE DECIDED THAT THE FMS WOULD NOT BE USEFUL ANY MORE. AFTER TELLING ATC THAT WE HAD MALFUNCTIONING AVIONICS; WE TOOK A HDG PROCEED TO AN EXTENDED FINAL AND CONTACTED MAINT ON THE GND. WE SUSPECTED THAT DUE TO HAVING 5 ELECTRICAL SENSITIVE MEL'S ON THE PLANE; THEN REDUCED TO 4 WE THOUGHT THAT MAYBE THEY COULD BE CONNECTED. WITH OVER 15-20 COMBINED YRS BTWN THE 3 PLTS IN THE COCKPIT; ALL OF US HAD NEVER SEEN ANYTHING LIKE THAT BEFORE. I HOPE THIS ISSUE GETS RESOLVED BEFORE ANOTHER FLT CREW ACCEPTS IT. RANDOM FMS BEHAVIOR; QUICK COMS BTWN CREW ALLOWED FOR IMMEDIATE COURSE REALIGNMENT; AND USING 'GREEN WORLD' TECHNOLOGY.