FLC OF A B737-300 FAILED TO FOLLOW ATC INSTRUCTIONS AND TURNED BASE LEG PRIOR TO ATC REQUEST CAUSING A LOSS OF SEPARATION WITH A B767 ON FINAL FOR ANOTHER SET OF PARALLEL RWYS.

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APCHING THE SMO VOR WE WERE TOLD TO 'DEPART SMO ON THE 68 DEG RADIAL FOR THE STADIUM VISUAL -- DSND AND MAINTAIN 3500 FT MSL.' WHILE ON THE 68 DEG WE WERE GIVEN SPD REDUCTIONS AND TOLD THAT A B767 WOULD BE LNDG ON RWY 24L AND WE WERE GOING TO RWY 24R AT LAX. APCH THEN TOLD US TO AMEND ALT TO 4500 FT MSL -- WE COMPLIED. THE 'STADIUM VISUAL' CALLS FOR A BASE TURN AT SMO 68 DEGS/9 DME. WE THOUGHT THAT WE HAD THE B767 IN SIGHT. (THE ACFT WE SAW WAS ACTUALLY LINED UP FOR ONE OF THE 25 RWYS). THE CAPT AND I THOUGHT WE WERE CLRED FOR THE 'STADIUM VISUAL' SO AT 9 DME WE TURNED BASE. EVIDENTLY WE WERE NOT CLRED TO TURN BASE. IMMEDIATELY AFTER MAKING OUR BASE TURN; APCH CTL TOLD US TO MAKE AN IMMEDIATE R TURN DIRECT TO THE FIELD. WE WERE NOW MAKING A DIAGONAL TO THE APCH END TO KEEP AWAY FROM THE B767 ON THE PARALLEL. AFTER MAKING THE TURN TOWARD THE FIELD THE CAPT SAID 'WE WERE EXECUTING THE 'STADIUM VISUAL' AS CLRED.' THE CTL RESPONDED BY SAYING; 'ROGER; I WAS ENSURING SEPARATION.' THE REST OF THE APCH WAS UNEVENTFUL. UPON LNDG WE WERE TOLD TO CALL SOCAL APCH AND INFORMED OF THE LOSS OF SEPARATION.