AN INSTRUCTOR PLT RPTS FLYING THROUGH A PARACHUTE DROP AREA THAT WAS INCORRECTLY ANNOUNCED BY THE PLT MAKING THE DROP.

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FLYING R-HAND TFC PATTERN AT BYRON WITH A STUDENT; WE WERE ADVISED OVER THE CTAF THAT SKYDIVERS WOULD BE FALLING NE OF THE DEP END OF RWY 30 (RWY IN USE). IN RECENT EXPERIENCE; I HAVE ALWAYS KNOWN THE PARACHUTES TO DROP NW OF THE RWY; IN ORDER TO REMAIN CLR OF THE R-HAND PATTERN. THE SKYDIVING PLANE AGAIN RPTED JUMPERS FALLING NE OF THE RWY; SO FOLLOWING THROUGH WITH MY TOUCH-AND-GO I STATED THAT I WOULD MAKE L TFC 1 TIME AROUND IN ORDER TO AVOID THEM. ALREADY IN THE L XWIND TURN; I SAW JUMPERS ABOVE AND DIRECTLY AHEAD. KEEPING THE TURN IN TIGHT; I HEARD SOMEONE ON THE CTAF STATE; 'ANYONE WHO MAKES L TFC AT BYRON WILL BE SITTING IN THE FSDO WITH ME!' I BASED MY DECISION OF L TFC ON THE SKYDIVING PLANE'S REPEATED STATEMENT OF JUMPERS FALLING TO THE NE OF THE DEP END OF THE RWY WITHIN A MI OF THE ARPT. HE LATER CORRECTED HIMSELF AND SAID NW; BUT THAT WAS AFTER I HAD COMPLETED L TFC. WE STAYED IN THE PATTERN FOR ANOTHER 20 MINS OR SO AND DEPARTED BACK TO OAKLAND WITHOUT FURTHER OCCURRENCES. I GENERALLY STAY AWAY FROMM THE BYRON ARPT; ESPECIALLY WHEN PARACHUTE ACTIVITY IS BEING CONDUCTED; BUT THAT PARTICULAR DAY THE XWIND WAS EXCELLENT FOR TRAINING. MY RECOMMENDATION FOR A PROB SUCH AS THIS IS TO DROP SKYDIVERS FURTHER FROM THE ARPT. IT MAY REQUIRE THAT A VAN MEET THEM TO BRING THEM BACK TO THE ARPT; BUT IT SEEMS A SMALL PRICE TO PAY FOR SAFETY.