Cat urinating on rugs

Can anyone tell me why my cat urinates on my rugs. I know she has asthma, which she gets meds for. Cat box is clean, have tried different litters, thought maybe she punishes me for leaving her, but I've been home for a full week, and still she urinates on my rugs. I am thankful that she urinates on the rugs and not on my carpet, but I would dearly like to know why. She's been doing this for some time. I would take her to the vet, but she hates him (actually, I don't think he is a cat fancier) so I agree with her! Need to find a new one. I actually have two cats, both 7 yr old , but only have this problem with the one.