There are a number of 1 person Ken no Kata. Here is one example.

Movie of the kata.

See below for a printer friendly description of this kata.

Walk to the centre of the mat, facing the sensei, kneel into seiza and perform a rei.	Step up onto your right foot (left knee on the ground), drawing your sword …	… as if cutting an opponent horizontally across the stomach.
Stand upright, feet together, turning the sword to prepare for a downward diagonal strike, bringing your left hand to also grip the sword.	Step your right foot forward and bring the sword across your body in a downward diagonal motion, …	… as if cutting an opponent from collarbone to hip.
Step your right foot back and bring the sword across your body …	… as if cutting an opponent horizontally across the stomach, once again …	... contd.
Slide your left foot back to bring your feet square, bringing the sword across your body and up into the guard position, holding the sword with your right hand only.	Bring the sword down across the front of your body in a swift motion - to shake off the blood.	Re-sheath the sword…
… contd …	… contd …	… contd …
Kneel and rei.

There are a number of 1 person Ken no Kata. Here is one example.

Album with photos/movie of the kata.

Album with photos and movies of the kata.

See below for a pdf version for offline viewing and improved printing.