FALCON 2000EX FLT CREW HAS A CREW ADVISORY SYS MESSAGE 'BOTH BRAKE SYS' AFTER TKOF.

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OUR DAY STARTED OUT AS AN EARLY MORNING DEP OUT OF ZZZ TO POS THE ACFT FOR PAX PICK-UP. THERE WERE 2 OTHER CREW MEMBERS BESIDES MYSELF TO EXTEND OUR DUTY TIME FOR THE DAY. ONE OF THE CREW MEMBERS WAS NEW TO THE ACFT AND WAS ON THEIR FIRST PAX FLT. ALL AVIONICS BOOTED NORMALLY AND NO ABNORMAL CREW ADVISORY SYS MESSAGES WERE DISPLAYED DURING ENG START OR TAXI. ALL PREDEP CHKLISTS WERE COMPLETED AND WE DEPARTED RWY 24. AT THE TIME OF DEP I WAS RIDING IN THE JUMPSEAT; THE PIC WAS IN THE R SEAT AND THE CREW MEMBER NEW TO THE ACFT WAS IN THE L SEAT OPERATING AS PF. TKOF ROLL WENT SMOOTH AND THE ACFT OPERATED NORMALLY UP TO 400 FT AGL. AS THE GEAR COMPLETED ITS RETRACTION CYCLE AT ABOUT 500 FT AGL; AN AMBER 'FAULT CODE' MESSAGE APPEARED IN THE CREW ADVISORY SYS CLOSELY FOLLOWED BY A RED 'BOTH BRAKE SYS' CREW ADVISORY SYS MESSAGE. INITIAL CLB WAS CONTINUED TO OUR ASSIGNED ALT OF 4000 FT MSL. WE NOTIFIED ATC OF OUR ISSUE AND ASKED FOR PRIORITY HANDLING BACK TO RWY 24. AT THIS POINT THE PIC ELECTED TO LAND THE ACFT AND I MOVED INTO THE R SEAT TO HANDLE THE PNF DUTIES. FROM OUR SYNOPTIC PAGES WE DETERMINED EMER BRAKING WAS AVAILABLE ALONG WITH THRUST REVERSE; SO WE DECIDED NOT TO DECLARE AN EMER. THE 'BOTH BRAKE SYS' ABNORMAL CHKLIST AS WELL AS ALL NORMAL CHKLISTS WERE COMPLETED AS WE WERE VECTORED FOR A LONG FINAL TO RWY 24. UPON TOUCHDOWN; THE ACFT SLOWED USING NORMAL BRAKING AND NO USE OF THE EMER SYS WAS NEEDED. THE ONLY SYS UNAVAILABLE TO US WAS ANTI-SKID. WE TAXIED BACK TO THE RAMP UNDER OUR OWN PWR WITH CFR FOLLOWING BEHIND US AS A PRECAUTION. MAINT CAME TO OUR ACFT AND RESET THE BSCU (BRAKE/STEERING CTL UNIT) COMPUTERS; CHKED ALL FAULTS; INSPECTED THE ENTIRE BRAKE SYS; NOTED THE ISSUE IN THE MAINT LOGBOOK AND RE-DISPATCHED THE ACFT TO US WITH NO FAULTS. ALL PROPER PAPERWORK WAS COMPLETED AND THE FIX WAS PROPERLY SIGNED OFF BY A LICENSED A&P/IA MECH. THE FLT CONTINUED 1 HR 45 MINS LATER WITH NO FURTHER ISSUES FOR THE REST OF THE DAY (5 LEGS TOTAL).