A more thorough explanation:

SELF-MURDER

Self-murder is another term for suicide, which is the act of intentionally taking one's own life.

Example 1: John committed self-murder by jumping off the bridge.

Example 2: The high rate of self-murder among teenagers is a growing concern.

These examples illustrate how self-murder is another way of saying suicide. In the first example, John intentionally took his own life by jumping off the bridge. In the second example, the high rate of self-murder among teenagers refers to the alarming number of young people who are taking their own lives.