A B737-700 EXPERIENCED A CABIN ALT WARNING HORN AND EXCESSIVE CABIN ALT. THEY DECLARED AN EMERGENCY AND EXECUTED AN EMERGENCY DESCENT.

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WE HAD JUST BEGUN A DSCNT OUT OF FL410 WHEN WE RECEIVED A CABIN ALT WARNING HORN. WE DONNED THE OXYGEN MASKS AND ESTABLISHED COM BTWN US. MY FO DECLARED AN EMER. NEXT WE BEGAN AN EMER DSCNT. I WAS FLYING AND MY FO RAN THE CHKLIST. WE RECEIVED A CLRNC TO DSND TO 10000 FT SO WE CONTINUED TO THAT ALT. AFTER RUNNING THE CHKLISTS WE DECIDED TO CONTINUE TO ZZZ; WHICH WE FELT WAS THE BEST CHOICE OF LNDG ARPTS CONSIDERING OUR ALT AND LOCATION. THE APCH AND LNDG WERE UNEVENTFUL. THE ONLY INDICATION THAT WE HAD A PROB WAS THE INTERMITTENT WARNING HORN AND THE CABIN ALT NEEDLE. THERE WERE NO CAUTION LIGHTS OR OTHER INDICATIONS OF THIS EVENT. DURING THE DSCNT I NOTED THE CABIN ALT SLIGHTLY ABOVE 11000 FT. THE PAX OXYGEN MASKS DID NOT DEPLOY. NO INJURIES WERE NOTED AMONG THE PAX OR CREW. SUPPLEMENTAL INFO FROM ACN 786894: WE RAN THE CABIN ALT WARNING HORN CHKLIST AS WELL AS THE EMER DSCNT CHKLISTS. THE FREQ WAS CONGESTED SO I SQUAWKED 7700. THE CTLR THEN CALLED US AND ASKED THE NATURE OF OUR EMER; NUMBER OF SOULS ON BOARD AND AMOUNT OF FUEL WE HAD. I REQUESTED A DSCNT TO 10000 FT AND WE WERE GIVEN THAT LIMIT.