Rinsing the cat once or twice a week with distilled water will remove the allergen. It isn't the hair itself, but the reaction the hair has with the cat saliva when they groom themselves that is the allergen. And the reason it takes so long to remove the cat hair from a home with a vacuum cleaner is they spew the stuff right back out as you vacuum. That is why, even if you have a HEPA filter, you should always dust (what is that?) after using the vacuum cleaner. They cause dust and allergens to become airborne, only to settle over everything later.