When walking down an incline there is greater acceleration due to gravity. In order to maintain a walking speed, a braking force is needed to counteract the acceleration, and this braking force is given by the contact force of the initial footfall of each step as it's in front of your center of mass creating a force vector pointing away from your direction of acceleration. When going down a slope it's much more difficult for your initial footfall to be in front of your center of mass due to the limited reach of your legs as well as it being easier for your center of mass to pass in front of your supporting legs creating unbalance and downward acceleration. In addition your legs will more often be behind your center of mass than in front creating additional torque on your body that also has to be countered by your braking force.
There are several ways to counter each of these variables that cause you to lose balance. * Taking shorter steps will broaden the range of your braking force vector (relative to your center of mass) and will help prevent overextending your legs to better prevent your center of mass from passing too far in front of your supporting legs. 174
Depending on your speed this may not be viable since shorter steps will require an increased frequency of steps. * Lowering your center of mass will also help as then your legs can reach the ground sooner than from a higher position and thus create a braking force sooner and stronger with a broader range for your braking force vector and increase the distance your center of mass has to travel before being in front of your supporting legs. * Debatable, but walking backwards may help as some may find it easier to lower your body closer to the ground with one leg supporting your center of mass and have one leg extending backwards to provide the braking force than facing forward and having one leg extended forwards. The downside may be that if the torque on your body is great enough to cause you to rotate backwards it may more difficult to catch yourself and recover than if you're rotating forwards. This likely varies per person and the slope/walking situation at hand. 174