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Yep, keep pinching off thoseYep, keep pinching off those flower buds. Your basil's reproduction in shutting down due to heat or humidity. You could even cut off half the plant (make some pesto) and it should rejuvenate the basil for more growth.

2015 Special Edition Garden GuideCooking Fresh with The Old Farmer's AlmanacThe Almanac Monthly Digital MagazineWhat the heck is a Garden Hod?