B737-300 ON RWY 24L HOLTZ RNAV SID DEP FROM LAX TURNS AWAY FROM SID TRACK WHEN AUTOPLT ENGAGED.

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AFTER CONFIRMING OUR INITIAL FIX (DLREY ON THE HOLTZ 7 DEP) WE WERE CLRED ONTO POS AND HOLD ON RWY 24L. WE UPDATED OUR POS ON THE CTRLINE OF RWY 24L WHILE WAITING FOR TKOF CLRNC. THE TKOF WAS MINE AND WAS UNEVENTFUL FOR A COMPANY PROCS RNAV DEP UNTIL AUTOPLT ENGAGEMENT AT 1000 FT AGL. I RECONFIRMED THAT LNAV WAS ENGAGED BOTH ON THE BUTTON AND ON THE SCOREBOARD BEFORE ENGAGING THE AUTOPLT. AT AUTOPLT ENGAGEMENT; THE ACFT IMMEDIATELY BANKED TO APPROX A 25 DEG BANK L TURN. THE RAW DATA INDICATED THAT DLREY WAS STRAIGHT AHEAD OFF OF THE DEP END AND SHOWED THAT WE WERE ALREADY ON THE CORRECT COURSE AT AUTOPLT ENGAGEMENT. I QUICKLY DISENGAGED THE AUTOPLT AND CORRECTED WITH THE SAME BANK TO THE R TO GET BACK ON COURSE FOR THE DEP. I AM NOT CERTAIN HOW FAR L WE ACTUALLY TURNED; BUT MY GUESS WOULD BE ABOUT 15 DEGS. AFTER WE BEGAN THE TURN BACK TO COURSE; DEP CTL CALLED AND ASKED OUR HDG BECAUSE TWR CTL HAD CALLED THEM TO TELL THEM THAT WE HAD BEGUN A L TURN. WE TOLD HIM THAT WE WERE CORRECTING BACK TO COURSE AT WHICH TIME HE GAVE US A 210 DEG HDG AND WE CONTINUED THE DEP USING RADAR VECTORS. MY FO AND I BOTH REVIEWED THE EVENT AND WE HAVE BOTH DETERMINED THAT WE ACCOMPLISHED THE CORRECT COMPANY PROCS FOR THE DEP WE WERE EXECUTING. NEITHER ONE OF US WOULD HAVE DONE ANYTHING DIFFERENTLY. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR REITERATED THE CONVICTION THAT ALL PROCS WERE PROPERLY FOLLOWED AND THAT THE L TURN WAS BEGUN AWAY FROM THE DISPLAYED TRACK TO DLREY. DEP CTL PROVIDED RADAR VECTORS FOR THE BAL OF THE DEP PROC AND THE FMS FUNCTIONED PROPERLY FOR THE REMAINDER OF THE ENRTE AND ARR SEGMENTS OF THE FLT.