If a cat is held upside down and dropped, it is able to execute a twist and to land upright, even if it has no initial angular momentum.

To Quote from Conceptual Physics by Paul G Hewitt:

“Zero-angular momentum twists and turns are performed by turning one part of the body against the other. While falling, the cat rearranges its limbs and tail several times to change its rotational inertia (moment of inertia) repeatedly until it lands feet downward. During this maneuver the total angular momentum remains zero. When it is over, the cat is not turning. This maneuver rotates the body through an angle, but it does not create continuing rotation. To do so would violate angular momentum conservation”