A B727 DSNDING INTO SAT; TX; TURNS PREMATURELY TOWARD THE W AND TRACON REMINDS THEM TO KEEP FOLLOWING THE ARR.

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I WAS THE PF AND LEVELING OFF AT 12000 FT BY MARCS INTXN WHEN APCH CALLED US AND TOLD US TO TURN TO A 290 DEG HDG AFTER REACHING A FIX. I DID NOT UNDERSTAND FROM THE XMISSION WHICH FIX. THE PNF (CAPT) READ BACK THAT WE WERE TO TURN TO A 290 DEG HDG UPON REACHING MARCS INTXN. THE CTLR DID NOT RESPOND TO THIS READBACK. I TURNED THE ACFT TO A 290 DEG HDG AT MARCS. A FEW MOMENTS LATER; THE CTLR SAID SOMETHING TO THE EFFECT THAT WE HAD PREMATURELY TURNED TO 290 DEGS. HE GAVE US NEW INSTRUCTIONS AND WE PROCEEDED WITH AN UNEVENTFUL ARR AND LNDG. AFTER THE FLT; THE CREW DISCUSSED WHAT HAD HAPPENED. ONE CONCLUSION WAS THAT APCH HAD TOLD US TO TURN TO 290 DEG HDG AT CRISS INTXN AND NOT MARCS INTXN AS WE HAD READ BACK. SUPPLEMENTAL INFO FROM ACN 379715: THE CTLR THEN GAVE US TURN TO A HDG OF 290 DEGS (HE MEANT OR SAID CRISS). IT SOUNDED LIKE MARCS TO US. WE READ BACK 290 DEGS AT MARCS AND AT THAT TIME WE WERE AT MARCS SO WE TURNED TO 290 DEGS AND STARTED OUR DSCNT. 1 MIN LATER; THE CTLR CAME BACK AND ASKED US IF WE WERE STILL ON HDG. WE SAID NO; WE WERE FLYING 290 DEGS. CTLR THEN GAVE US INSTRUCTION TO HEAD STRAIGHT TO CRISS; BUT THEN CHANGED THAT TO HEAD STRAIGHT TO THE VOR AND AT 2 DME TURN TO 290 DEG HDG. SO WE READ THAT BACK AND NOTHING WAS SAID ABOUT ANY CONFLICT OR PROB.