FALCON 2000 FLT CREW INITIATED CLB FROM 1500 FT TOO EARLY ON TEB DEP.

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AFTER BEING CLEARED FOR THE TEB 5 DEP OFF RWY 24; I; THE PIC BRIEFED THE DEP PROC; WHICH IS QUITE COMPLEX; WITH THE SIC. THE DEP PROC INVOLVES FLYING THE RWY HDG TO A LEVEL-OFF AT 1500 FT MSL; FOLLOWED BY A HDG TURN TO 280 DEGS WHILE MONITORING DISTANCE TO A POINT 4.5 DME FROM THE VOR; FOLLOWED BY ANOTHER SHORT CLIMB TO 2000 FT MSL. AFTER LEVELING OFF AT 1500 FT MSL; AND WHEN THE CDI (BASED ON FMS INPUT) TURNED TO THE NEW HDG; I INTERPRETED THIS AS THE TIME TO START THE CLB TO 2000 FT MSL; INSTEAD OF ENSURING THAT THE ACFT HAD PASSED THE 4.5 DME POSITION. I DO NOT BELIEVE THAT THE ACFT WAS MORE THAN ABOUT 120 FT INTO THE EARLY SECOND CLB SHORT OF THE 4.5 DME BEFORE ATC CLRED US TO 6000 FT MSL. I BELIEVE THERE ARE A FEW CHANGES THAT COULD HELP SAFEGUARD REOCCURRENCES. THESE INCLUDE METHODICALLY REVIEWING THE DEP PROCS; MAKING USE OF THE AUTOMATION SOONER IN THE SEQUENCE OF EVENTS (ENGAGING THE AUTOPILOT SOONER); AND POSSIBLY REEVALUATING THE DEP PROC ITSELF. BECAUSE OF THE COMPLEX NATURE OF TEB'S DEP PROCS; I SUSPECT THAT UNINTENTIONAL DEVS FROM IT ARE A COMMON OCCURRENCE.