How old is she? A month isn't the norm, but you can have swelling for a week or 2 after the heat. When in doubt, see your vet.
If questions, see a Vet... however Basenjis heat cycle is 1 month.... heaviest bleeding is 3 week
It's normal, I even had a bitch that was bred on day 31 and she had a litter of five.
As Deborah is suggesting, you haven't laid out what you mean by being in season. Heavy bleeding for over a month? A discharge which is decreasing? Swollen vulva? Dogs are variable, so what is normal for one may not be normal for another, and even what is normal for one may not be normal every year. Does she usually go in season in the summer? Is this her second season of the year? Did she have pups last cycle? More importantly, how old is she? A prolonged heat in a young female is likely no big deal, but in a mature female may be caused by a cyst or a tumor. So I'd probably take her to the vet.
@donc - Note that Basenjis typically do NOT have 2 seasons a year. Only 1 is mostly the normal. Many will have a season after whelping, but they are also typically not fertile
@tanza -- I know. They also don't typically have one in June, which is why I was asking about whether she had whelped last cycle. I don't think we have a lot to go on. Not being critical, but "my dog seems to be in heat for over a month" doesn't provide a lot of information and could mean a lot of different things.