Diabolo suicides are tricks where you let go & recatch a handstick in some way. The outside unwrap suicide is very different from a Straight Suicide & is the opposite of the Inside wrap suicide.
Get the diabolo spinning then wrap the string once around the axle by circling the tip of your dominant handstick around the cup closest to you. Don't pull too tightly on your dominant handstick. Hold your subordinate hand at around shoulder height with your palm facing down so that the handstick's tip points towards the diabolo & the handle points out to the side. Hold your dominant stick down at waist height so that the diabolo is directly below it. This will insure that the diabolo doesn't travel down the string, for the move to work smoothly the diabolo needs to be as close to the tip of your dominant handstick as possible.
Let go of the subordinate handstick, at the same time smoothly lift your dominant handstick up to shoulder height to prevent the released stick from hitting the ground. The subordinate stick will swing round in a circle underneath the diabolo unwrapping the string from the axle. As the stick swings underneath the diabolo & starts to swing up again lower your dominant handstick & pull it backwards so that the released handstick passes in front of the string. Catch the released stick as it passes over the diabolo in your subordinate hand. If the stick passes behind the string the string will be twisted twice, to exit swing an Sun in front of the body to your subordinate side.
Lowering the dominant handstick is very important for two reasons. One, it slows the swing of the released stick making it easier to make the final catch. Also the moment you release the subordinate handstick the diabolo starts to roll down the string pulling the released stick in towards the axle. If the handstick touches the diabolo it will slow it down & cause it to severely tilt. Lowering the dominant handstick reduces the pull of the diabolo, giving you more time to complete the move.
A good sequence to put this move into is: Straight suicide releasing the dominant handstick, Inside wrap suicide again releasing the dominant handstick (which wraps the string around the axle for you) then outside unwrap suicide. For extra style points when throwing the inside wrap suicide catch the released stick under the leg & pull the outside wrap suicide out the other side.