A natural way to remove pet urine from your carpet is to mix some baking soda and apple cider vinegar or plain vinegar together.
Make a paste out of the baking soda and Apple Cider Vinegar or plain vinegar and apply the paste to the carpet where the pet urine is and leave it overnight.
Then run a carpet cleaner over the carpet the next day to remove the baking soda paste and pet urine from the carpet.
You can also buy some pet urine neutralizer at Walmart or pet stores and spray the carpet with the Pet Urine Neutralizer and mix some in with a carpet cleaner and it will also get rid of the pet urine and remove the odor of pet urine from your carpet.