A B737-300 IS ALLEGED TO HAVE TURNED TOO SOON PRIOR TO IDALE INTXN BY THE OBSERVING DEP CTLR AT LAS; NV.

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FLT XXYY LAS-MDW CLRED ON THE AACES RNAV 1 DEP BRYCE CANYON TRANSITION. THE FMC WAS PROGRAMMED AND RTE OF FLT CHKED DURING PREFLT. FMC POS WAS UPDATED AT THE END OF RWY 25R AND ACTUAL REQUIRED NAV PERFORMANCE SHOWED .36 NM. ACR Y (B737) HAD DEPARTED FOLLOWED BY COMPANY AND THEN WE WERE CLRED TO TAKE OFF AND KEEP COMPANY AHEAD IN SIGHT. WE WERE AWARE COMPANY WAS ENRTE TO LAX BUT DID NOT KNOW THE DEST; RTE OF FLT; OR DEP FOR ACR Y FLT. LNAV WAS SELECTED AT APPROX 1000 FT AGL. THE FLT DIRECTOR AND HSI SHOWED US ON COURSE TO THE FIRST FIX; LODZY. THE LEGS PAGE WAS MONITORED ON THE CDU. AUTOPLT WAS ENGAGED AT APPROX 2000 FT AGL. THE ACFT EXECUTED THE TURN TO ANDDY APCHING LODZY; AND EXECUTED THE TURN TO IDALE APCHING ANDDY. ENRTE TO IDALE BOTH COMPANY AND THE PRECEDING FLT WERE IN SIGHT. WE WERE INITIALLY CLRED TO 7000 FT AND WERE CLRED TO 8000 FT ENRTE TO IDALE. APPROX 2.5 MI PRIOR TO IDALE THE ACFT STARTED THE TURN FOR HITME. BOTH PLTS TOOK NOTE OF THE TURN AND ATTRIBUTED THE LEAD TO THE TURN BEING 84 DEGS. I ALSO TOOK NOTE OF THE ACR Y FLT ABOVE US TO THE S; NOW HEADED E. AT THIS POINT LAS VEGAS DEP CALLED TFC AT 12 O'CLOCK POS AND I ACKNOWLEDGED THE CALL. DEP THEN TOLD US TO TURN L TO 070 DEGS AND MAINTAIN 230 KTS. THEY SAID WE HAD CUT THE CORNER TOO MUCH AT IDALE. DEP THEN TOLD US TO TURN R TO 150 DEGS FOR SPACING AND CLB AND MAINTAIN 13000 FT. DEP THEN GAVE US A PHONE NUMBER TO CALL WHEN WE REACHED OUR DEST. AFTER A COUPLE OF MINS WE WERE CLRED DIRECT TO AACES THEN FLT PLANNED RTE; COMPLY WITH THE RESTRS ON THE DEP; CLB TO FL190 AND NORMAL SPD. THE REMAINDER OF THE DEP WAS WITHOUT INCIDENT. SUPPLEMENTAL INFO FROM ACN 536158: AFTER SWITCHING TO ZLA; I CALLED DEP ON 133.95 ON VHF #2 AND ASKED HIM FOR THE REASON FOR THE CALL. HIS REPLY WAS THAT WE HAD TURNED EARLY. ARRIVING AT MDW; I CALLED AND SPOKE WITH THE SUPVR. HE WAS CORDIAL; AND IS NOT GOING TO 'FILE ANY PAPERWORK.' HE JUST WANTED TO DISCUSS THAT WE TURNED EARLY; AND ROLLED OUR TURN TO HITME. THE LNAV APPEARED TO BE PROPERLY FUNCTIONING. I HAVE FLOWN THIS DEP WITH NO PROBS. I WAS BUSY WITH THE VECTORS/AIRSPD/ALT AFTER THE TURN AND DID NOT HAVE THE TIME TO CHK THE REQUIRED NAV PERFORMANCE TO SEE IF WE WERE ACTUALLY IN THE INCORRECT PLACE. SINCE THE SUPVR IS NOT GOING TO TRY TO VIOLATE US; PLEASE USE THIS AS INFO/DISCUSSION WITH LAS DEP. MAYBE WE AS PLTS NEED SOME HELP OR UNDERSTANDING OF THIS NEW PROC.