FLC'S OF BOTH ACFT SHUT OFF THEIR TAXI LIGHTS TO HELP NOT 'BLIND' THE OTHER RESULTING ON A NEAR MISS COLLISION NEAR THE HOLD SHORT AREA AT THE RWY.

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CLRED TO TAXI TO RWY 4L FROM RAMP (GATE) VIA TXWY K TRANSITIONED TO END OF RWY AT K1 WHICH IS FREQUENTLY REQUESTED BY ATC. AS ACR Y 737 WAS TAXIING S DOWN A 'A' TXWY OUR TAXI LIGHTS WERE ALL ON AND LIGHTS WERE ALL ON AS WE TURNED TO TRANSITION TO THE END OF THE RWY ON K1. AS WE MADE THE TURN ACR Y SHUT OFF ITS TAXI LIGHTS (IT APPEARED SO AS TO NOT BLIND US; AND WE DID THE SAME). (BOTH ACFT CONTINUED TO DISPLAY ALL REQUIRED NIGHT POS LIGHTS.) WE WERE TAXIING SLOWLY BUT SUDDENLY ACR Y SEEMED TO PICK UP ITS SPD AND IT BECAME APPARENT THAT THEY DIDN'T SEE US. I ADVANCED THE PWR LEVEL ON THE L ENG AND MADE A RAPID TURN TO THE R (ONTO 'A' BY DEP END OF RWY 4L) (ACR Y) WING APPEARED TO MISS MY WINDSHIELD BY ABOUT 10 FT. I AM QUITE SURE HE NEVER SAW ME. GND NEVER SAID ANYTHING TO US NOR DID TWR WHEN WE SWITCHED OVER TO THEM. I SHOULD NOT HAVE TURNED ON K1 -- COULD HAVE TURNED ON RWY K AND THAT WOULD HAVE AVOIDED THE WHOLE INCIDENT. BUT EVEN MORE IMPORTANTLY; ACR Y SHOULD HAVE BEEN LOOKING WHERE THEY WERE GOING WHICH THEY OBVIOUSLY WEREN'T. HAD I NOT MADE A QUICK TURN; WE DEFINITELY WOULD HAVE COLLIDED.