Does she only urinate on the rug? She doesn't urinate on anything else? If the rug isn't in the bathroom, does she urinate in other places? Is the rug in the same bathroom as the litter box? How often do you scoop/change the litter? Have you changed the litter (i.e. brand) recently? Are there other cats in the household?
The answers to these qustions could provide clues to why she's urinating on the rug.
There is a product called Feliway that you could try spraying on the rug to discourage her urinating fetish.
She lives with another little boy cat. There are 2 litter boxes in the bath room. I try to keep them very clean. She urinates on the bath rug and another small rug outside the bathroom.
Many cats have a fetish about textures and smells. I had a cat that loved to pee on plastic. Could be that the smell of the rug irresistible, and she can't help herself. Other causes are hateful peeing due to anxiety from other cats or humans, bladder problems,and diabetes. Your cat seems to like/hate the smell of the rug. Is it blue?