AN IFR BEECH-90 HAD A NEAR MISS WITH A VFR FALCON JET NEAR PSP.

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AFTER RECEIVING MY CLRNC DOWN TO 4000 FT I HEARD A FALCON JET CHK-ON WITH PALM SPRINGS APCH. THE FLACON HAD JUST DEPARTED UDD AND WAS CLBING THROUGH 1300 FT REQUESTING AN IFR CLRNC. APCH'S REPLY TO THE FALCON WAS TO STAND-BY FOR HIS CLRNC AND MAINTAIN VFR. APCH THEN RPTED THE FALCON TFC TO ME; AND ALTHOUGH I WAS ALREADY TRYING TO FIND THE FALCON; THE HAZE AND DISTANCE MAKING IT EXTREMELY DIFFICULT; I RPTED TO PSP APCH NEGATIVE CONTACT. ABOUT 1 MIN LATER; PSP APCH CALLED THE FALCON TFC TO ME AGAIN; I RPTED NEGATIVE CONTACT WITH THE FALCON AND THAT I HAD UDD IN SIGHT. A FEW MOMENTS LATER I ESTABLISHED VISUAL CONTACT WITH THE FALCON AT MY 1 O'CLOCK POS. AT THAT INSTANT; IT APPEARED THAT THE FALCON WAS CLBING AND WOULD PASS OF MY R SIDE. I CALLED PALM SPRINGS APCH AND SAID TFC IN SIGHT NO FACTOR. JUST AS I FINISHED MY RADIO XMISSION TO PSP APCH THE FALCON WAS IN A CLBING R TURN COMING DIRECTLY AT ME. I INITIATED EVASIVE ACTION TO AVOID THE FALCON BY MANEUVERING MY ACFT INTO A STEEP DIVING R TURN. UPON RECOVERING FROM MY EVASIVE MANEUVER; I CALLED PSP APCH AND TOLD THEM I HAD TO MANEUVER TO AVOID THE FALCON.