A FALCON 10 DEPARTING TEB EXCEEDED THE INITIAL 1500 FT LEVEL OFF ALTITUDE BY 300 FT.

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THE PROB AROSE WHILE FLYING THE RWY 24 DEP FROM TEB. I HAD STUDIED THE TEB 5 DEP THOROUGHLY PRIOR TO THE PAX ARRIVING AND ENGINE START. DURING TAXI TO RWY 24; THE CO-PLT AND I BRIEFED THE DEP AGAIN CLARIFYING TO EACH OTHER THE DETAILS OF THE PROC. ONCE WE WERE CLRED INTO POSITION AND HOLD; WE BRIEFED THE PROC ONE LAST TIME. THE CO-PLT SAID; 'CLB TO 1500 FT; AT 4.5 DME RIGHT TURN 280 DEGS; THEN UP TO 2000 FT.' MY REPLY WAS; 'NO; IT'S CLB TO 1500 FT; R TURN 280 DEGS TO 4.5 DME THEN UP TO 2000 FT.' THE CO-PLT DOUBLE CHKED THE DEP AND AGREED. THEN WE WERE CLRED FOR TKOF. AS WE WERE CLBING OUT; TEB TWR HANDED US OFF TO NY APCH. AFTER THE CO-PLT CONTACTED APCH; THE CTLR SAID; 'MAINTAIN 1500 FT HEADING 280 DEGS;' AS I WAS CLBING THROUGH IT TO 1700 FT AND MANAGED TO LEVEL AT 1800 FT AND BEGIN A DSCNT BACK TO 1500 FT. THE CO-PLT KEPT SAYING '1500! 1500!' SOMEWHERE BETWEEN THE FINAL BRIEFING BEFORE TKOF AND THAT POINT; MY MIND SOMEHOW SWITCHED TO AN INITIAL 2000 FT LEVEL OFF. IT WAS THEN I GOT IRRITATED AT THE CTLR FOR GIVING US A NEW ALTITUDE ASSIGNMENT AS WE WERE PASSING THROUGH IT; EVEN THOUGH HE DIDN'T GIVE US A NEW ONE. THE CTLR RETORTED THAT THE DEP WAS TO MAINTAIN 1500 FT AND I SHOULD READ THE DEP WHEN I GOT TO ALT. AFTER HIS RETORT; I REALIZED MY ERROR AND APOLOGIZED. THINKING ABOUT THE EVENT DURING CRUISE; I THINK THE REASON I CONTINUED THE CLB WAS THE LAST ALT I BRIEFED PRIOR TO TKOF. TALKING IT OVER WITH THE CO-PLT; MY SOLUTION WAS THAT I SHOULD HAVE STATED; 'CLB AND MAINTAIN 1500 FT; THEN RIGHT 280 DEGS.' A SUGGESTION FROM THE CO-PLT WAS THAT WE SHOULD PULL THE POWER BACK RIGHT AWAY WITH LOW ALTITUDE LEVEL OFFS. BUT EVEN THEN; MY MIND WAS SET ON 2000 FT BEING THE INITIAL LEVEL OFF. ALTHOUGH WE HAD BEEN ON DUTY ALREADY FROM OVER 12 HRS; I DO NOT BELIEVE FATIGUE WAS A FACTOR IN THIS CASE AS INDICATED BY MY CATCHING THE CO-PLT'S SWITCH OF THE HEADING AND DME BEFORE TKOF. BOTH THE CO-PLT AND I FELT QUITE ALERT AND REMAINED SO DURING THE REMAINDER OF THE FLT.