A C560XL DEPARTING TEB ON THE TEB DEP CLBED BEFORE CHARTED POINT TO 2000 FT.

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ON CLIMB OUT FROM TEB FLYING THE TEB 5 DEP THE FINAL CLIMB FROM 1500 FT MSL TO 2000 FT MSL WAS INITIATED EARLY. THE FMS WAS BEING UTILIZED AND THE AUTOPILOT WAS ENGAGED AT 400 FT. THE AIRCRAFT PROCEEDED ON THE DEP AS PUBLISHED TO 1500 FT MSL AND BEGAN THE RIGHT TURN TO A 280 DEG HEADING AS CALLED FOR BUT SHOULD HAVE LEVELED OFF AT 1500 FT TO THE 4.5 DME OF TEB BEFORE CLIMBING TO 2000 FT. INSTEAD OF HAVING SET THE INITIAL ALTITUDE OF 1500 FT AND THE RESETTING TO 2000 FT AT THE 4.5 NM FIX THE ALTITUDE PRESET WAS MISTAKENLY SET TO 2000 FT AT TAKEOFF THEREFORE THE AIRCRAFT CONTINUE THE CLIMB TO 2000 FT PRIOR TO THE 4.5 NM FIX. THE PNF DID NOT DETECT TO ERROR EITHER AND NO CALL OUT WAS MADE. CONTRIBUTING FACTORS WAS A DISCUSSION BETWEEN THE CREW PRIOR TO TAKEOFF ABOUT PAX HANDLING CREATING A DISTRACTION FROM A PROPER TAKEOFF BRIEF. THE AIRCRAFT WAS FOURTH IN LINE BUT WAS GIVEN A CLRNC TO THE RWY FOLLOWED QUICKLY BY TAKEOFF CLRNC. IT WAS UNEXPECTED TO RECEIVE THE CLRNC SO QUICKLY AND THIS HELPED CREATE A HURRY UP SITUATION AND VOIDED AN OPPORTUNITY TO ACCOMPLISH A FINAL REVIEW OF THE TAKEOFF PROC. IN ADDITION; FATIGUE WAS ALSO A FACTOR AS THE DAY BEFORE WAS A 13 HRS DUTY DAY PRECEDED BY A 12.5 HOUR DAY. FURTHERMORE; MUCH ATTENTION BY BOTH CREW MEMBERS IS BEING PAID TO THE AIRCRAFT BEING RELOCATED TO A NEW AIRPORT AND THE TASKS REQUIRED TO ACCOMPLISH IT. THE AIRCRAFT HAS FLOWN 400 HOURS YEAR-TO-DATE WHICH IS A VERY BUSY SCHEDULE FOR JUST TWO PILOTS.