I have an allergy to cats but I want to get a cat. Do you think there's any way to get a cat without allergy?

Not likely. Cat allergy is related to exposure to the two major components-cat dander (skin flakes) and saliva. Since it is impossible to avoid these materials if a cat is in the house, living with a cat is difficult for someone with cat allergy. A "hypoallergenic" was recently bred which may be tolerated by patients with the mildest symptoms. The cost was $4000 if i remember correctly.