every morning a female cardinal flys into our window. I don't know what to do

It's not good for the bird to keep doing this; many birds are killed this way.

If you have a wild bird feed store near you, they may sell silhouettes of hawks or other birds of prey that you can put on your window (they cling) to scare off the cardinal.

Or cut out a similar shape from a brown paper bag, or something, and duct-tape it to the outside of the window.

Here are other suggestions from a birding magazine that may give you ideas.

http://www.birdwatchingdaily.com/featured-stories/15-products-that-prevent-windows-strikes/

The poor bird sees her reflection in the window and thinks it's another bird.

I had a robin flying into a window. I finally put a big square piece of cardboard on the outside to block the reflection. That stopped the behavior.

On 2/16/2015 2blonde said:

The poor bird sees her reflection in the window and thinks it's another bird.

yes this. There are ways to prevent that from happening. Just google it!

We've had this happen many times - seems especially true with the cardinals. We had one who sat on the rear view window of our car every day for weeks. Unfortunately we left a window down for a while one day and a cat caught the bird inside the car. He was lunch. If I had another chance to handle this, I would bag the rear view windows and hopefully save the bird's life.

I would suggest that you get some cardboard pieces and tape them to the windows that the bird has an interest in. It probably wouldn't take long to discourage the bird and perhaps save him or her life.

The bird sees reflections of trees and such in the window and tries to fly toward them. The solution is to hang vertical cords on the outside of the window, about 4 inches apart. The birds will see the cords and not fly in that direction. It's called an Acopian BirdSaver (named after the inventor) and, while you can buy them from his website, he actually encourages you to make your own (it's easy!). I just heard about it on NPR.

Acopian BirdSaver

Ah, the poor little gal!

The cardinals are always the first to come to my feeder right outside my office window. I don't think they've ever flown into the window.

But every now & again there is a crash, boom or bang either from Mustache & company (the squirrels) vying for space on my ledge feeder or from some other kind of bird. The other day a hawk bammed into the window!

Before I married and left home, we had a male cardinal doing this at the basement window right below my bedroom window. He always flew into that same window, never any of the other basement windows. I was awakened to the sound of him slamming himself into the glass every morning at daylight. Mom taped a piece of cardboard over the inside of the window and he stopped. After mating season, Mom would take the cardboard down. For 3 years in a row we had this issue, and really thought it was the same bird. We named the cardinal Buster.