OPERROR OCCURRED WHEN TRAINEE CTLR DSNDED AN ACR B737 TO FL310 VICE FL330 WITH UNKNOWN TFC AT FL310. INSTRUCTOR CTLR ATTEMPTED TO REVERSE THE DSCNT BUT SEPARATION WAS LOST. B737 FLC RPTED SEEING AN ACFT (WHITE DOT) ON THE TCASII; NO TA OR RA RECEIVED.

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I WAS INSTRUCTING TRAINEE AT A HIGH ALT SECTOR. SHE MADE SEVERAL BAD DECISIONS; AND I TRIED TO OFFER ADVICE ON HOW TO FIX THE PROBS. THE LAST MISTAKE WAS HERS. BOTH I AND THE D SIDE CTLR TOLD HER TO DSND ACR X TO FL330. FOR SOME REASON; SHE ISSUED FL310; SAME ALT AS THE TFC. WE TRIED TO STOP THE DSCNT AT FL330; NO LUCK. SUPPLEMENTAL INFO FROM ACN 365919: WE WERE DSNDING THROUGH ABOUT FL323 WHEN CTLR ISSUED A CLRNC TO LEVEL AT FL330. WE INFORMED CTLR WE WERE THROUGH FL330 AND WE WOULD STOP DSCNT AND CLB BACK TO FL330. IT TOOK APPROX 400 FT FOR US TO CHANGE DSCNT INTO A CLB. AS WE ROUNDED OUT AT FL319 WE SAW AN ACFT (WHITE DOT; NO RA OR NO TA) APPEAR ON TCASII DIRECTLY BELOW AT FL310. SIMULTANEOUSLY; A NEW; DIFFERENT VOICE CAME OVER THE RADIO TELLING US HE NEEDS US AT FL330 RIGHT AWAY. WE ACKNOWLEDGED AND WE CLBED BACK TO FL330 AS HE SPOKE. THE EARLIER CLRNCS (FIRST VOICE -- FEMALE) HAD NO SENSE OR URGENCY OR DOUBT AS TO TIMBRE OR PATTERN. THE SECOND VOICE (MALE) WAS FIRM; BUT NOT PANICKY OR EXCITED. IT WAS PROBABLY THAT OF A MORE EXPERIENCED CTLR OR SUPVR.