A B737 FLC MISINTERPS THE CLRNC AND LEVELS OFF AT 4000 FT DURING A DEP PROC THAT HAD ISSUED A 10000 FT CLB OUT OF BUF; NY.

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FO OBTAINED CLRNC; READING BACK THE FOLLOWING: 'MIL M4000; R-HAND SQUAWK XXXX.' CLRNC DELIVERY RESPONDED AFFIRMATIVELY AFTER SOME DISCUSSION REGARDING THE SQUAWK. ON DEP; WE CONTACTED DEP CTL RPTING THAT WE WERE CLBING TO 4000 FT. SHE RESPONDED WITH 'MAINTAIN RWY HDG.' ABOUT 2 MINS LATER; THE DEP CTLR QUESTIONED IF WE WERE CLBING. WE RESPONDED THAT WE WERE MAINTAINING 4000 FT AS ASSIGNED. SHE (ATC) QUESTIONED WHO ASSIGNED US 4000 FT. WE STATED THAT WE WERE ASSIGNED 4000 FT FROM CLRNC DELIVERY. HER (ATC) RESPONSE WAS THAT SHE WOULD 'CHK ON THAT.' LATER THE SAME DAY; I CALLED THE BUF TRACON TO INQUIRE ABOUT THE CONFUSION ON OUR DEP. I WAS INFORMED AFTER SOME DISCUSSION AND REVIEW OF THE TAPES THAT THE CLRNC WAS TO CLB TO 10000 FT THE FO READ BACK 4000 FT AND THE CLRNC DELIVERY PERSON DID NOT DETECT THE ERROR. I READ THE CLRNC AS WRITTEN BY THE FO AND 4000 FT WAS WRITTEN DOWN. PREVENTION: 1) GREATER DILIGENCE BY ALL PARTIES CONCERNED. 2) DEP CTL CONFIRM ALT CLBING TO. 3) IF IN DOUBT (ANY DOUBT; NO MATTER HOW LITTLE); QUESTION AND CONFIRM!