A strap that prevents the horse from tossing his head too high, called a tie-down in Western parlance. There are two basic types, the standing martingale (more restrictive) and the running martingale (less restrictive).
The standing martingale consists of two straps: one strap that circles the base of the horse's neck, and another that runs from the back of a cavesson noseband, through a slit in the neck strap, to buckle around the saddle girth.
The running martingale attaches to the girth and the neck strap in the same way. Two straps come up from the neck strap, one attaching to each rein with a metal ring.
Both types of martingale should be carefully fitted.