One of the vital elements in improving your horse's way of going on the flat is to teach him to carry more weight over his back legs and less on his front.
A horse grazing in the field carries 70% of his bodyweight over his front legs, a horse performing a high school movement, such as levade, is momentarily carrying all his weight on his back legs. Even the most green and uneducated horse can physically shift his balance back - such as when he spooks, sitting almost down on his hocks to gain enough momentum to accelerate away from the terrifying plastic bag! Our aim in this exercise is to use transitions to teach our horse to gradually come into a better balance.
You want your horse to halt in self carriage, be very aware that you must not use the rein as the hand brake, but rather just transmit signals via the rein and the bit.
Remain stationary for a second or two, then ride forwards into a marching walk. You are riding into a corner now, and the act of riding positively forwards as the horse corners will encourage him to activate and engage his inside hind leg. Repeat this halt-walk transition before every corner. After a couple of circuits you should feel that your horse begins to anticipate the halt and soon your weight aid should be enough to instigate it. Equally he should begin to halt with the hind leg further under his body, in anticipation of the brisk forwards step that follows.
Repeat on both reins. You can progress this exercise by riding a trot-walk-trot transition before every corner and eventually a canter-trot-canter. You may find that at faster speeds it is not possible to ride a transition before every corner. It is far better to use every second corner in this case rather than give the horse stronger or conflicting signals.
Repetition of this exercise harnesses the horse's ability to anticipate signals. This is not a bad thing- he should begin to respond to your weight signals and require less rein in the downward transitions, which leads to self carriage and engage the hind legs more in anticipation of the upward transitions, which will eventually lead to better balance.