According to the book Gross Motor Skills for Children with Down syndrome,
"walking on a balance beam will help to change your child's early walking pattern. In her early walking pattern, she will use a wide base, her hips will rotate outward causing her knees and fee to turn out, and she will take weight on the inside borders of her feet. By practicing walking on a balance beam, she will learn to walk with her legs and feet in a new position. She will learn to rotate her hips so her knees and feet point straight ahead."
As suggested in the book, we started out with a 1-inch thick x 8-inch wide x 6-foot long wooden board from our local home improvement store. I spray-painted stenciled numbers on ours since Matthew enjoys counting. It used to be an outside activity but I've since brought the boards indoors, in our hallway. Both kids enjoy walking on it whenever they are in the hallway.
Matthew has progressed to walking on the narrower 1-inch thick x 5.5-inch wide x 6-foot long board, mostly without assistance. I couldn't find the time to paint this board but it was equally enjoyable for both kids. Elizabeth walks along the narrower board with one foot on and one foot off. That's how Matthew started with the wider board.
The next step would be to walk on a 4-inch wide x 6-foot long (or longer) board, placing one foot in front of the other without assistance. I plan on getting a board that is at least 2 inches thick when he's ready for a bigger challenge. Being just a little bit higher off the ground can be scary for many kids. A 1-inch thick balance beam helps take away the fear of falling from a higher surface and focus the attention on walking within the set boundary.
These wooden boards also double as a racetrack for little horses or as a motor speedway.
Fancier (but more expensive) balance beams are also available from various retailers. Googling "balance beams for kids" on amazon.com will show many varieties of balance beams. The book "How To Teach Your Baby To Be Physically Superb" by Glenn Doman, Douglas Doman and Bruce Hagy has a detailed plan on how to make a sturdy, height-adjustable balance beam.
A word of caution: Leaving the boards in the middle of the hallway at night can result in stubbed toes. Bill learned that painful lesson one time at about 2am.