HAVING DIFFICULTY WITH LNAV AND AUTOPLT ON THE LAS COWBY ONE RNAV DEP A B737-300 CREW TURNS OVER THE 'FIXIX' FIX CAUSING A MINOR DEV NOTED BY AND CORRECTED WITH A VECTOR BY ATC.

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WE WERE ASSIGNED THE COWBOY DEP; EXPECTING RWY 25L. WHEN WE WERE CLRED TO TAXI; THE RWY ASSIGNMENT CHANGED TO RWY 19L. WE COMPLETELY REPROGRAMMED THE RWY AND DEP; VERIFYING THE FIXES ON DEP. AT 400 FT AGL; LNAV WAS SELECTED; AND 'LEGS PAGE.' AT 1000 FT AGL; I CALLED FOR 'FLAPS 1 DEG; CLB THRUST' AND SELECTED THE 'A' AUTOPLT. EVEN THOUGH THE 'LEGS PAGE' SHOWED THE TURN IN 4 MI; THE ACFT STARTED AN IMMEDIATE R TURN. I DESELECTED AUTOPLT AND RESELECTED HDG SELECT. WE CONTINUED THE DEP FLYING RTE MANUALLY WITH INFO FROM THE LEGS PAGE. OVERHEAD 'FIXIX' WE TURNED TOWARD ROPPR (FROM 190 DEGS TOWARD 235 DEG HDG). LAS APCH ASKED IF WE WERE IN TURN TOWARD ROPPR AND WE RESPONDED 'YES.' HE THEN ASSIGNED US A HDG OF 210 DEGS. WE WERE PASSING 200 DEG HDG WHEN THIS WAS ASSIGNED. THE DEV WAS MINOR; IF ANY; AND THE CTLR STATED THERE WAS 'NO PROB.' IN CONCLUSION; THE ACFT BEGAN A TURN ABOUT 4 MI EARLY. WE REVIEWED OUR SETUP AND PROCESS. EVERY FIX WAS LISTED AND IN THE APPROPRIATE ORDER; OFF THE APPROPRIATE RWY. THE PLT MONITORING WAS QUICK TO VERBALIZE THE ERROR OF EARLY TURN AND THE PF SIMPLY HAND FLEW THE COURSE.