http://www.youtube.com/watch?v=jeX_NkKFgGg
This assassination is similar to the Triple Jump:
http://www.youtube.com/watch?v=2OdKxPms9Vs
but the Quadruple Jump is more difficult due to the very precise timing requirements. After making a series of three jumps from the north buildings, Altair must land and roll on the execution platform at a specific time in order to avoid detection. The fourth and final jump occurs after the landing roll; Altair leaps and tackles Majd Addin head-on to make the kill. Pay special attention to Majd Addin's final words for some added humor.
I start the mission by killing the lower archer located north of the execution platform. This isn't necessary for any reason other than he would block the camera's view of Altair during the first jump. I continue to climb up to the starting point, and I use the Dome of the Rock as a nice background as I wait for the right moment. I start positioning myself for the jump when the "temptress" finishes her words. I don't just run off the edge of the building - I force an early leap by double tapping the legs button. As I fall, I pull back on the left stick and press grasp so that Altair reaches behind to catch the ledge. Then I relax the left stick and press jump so that the Altair pushes himself directly away from the wall. He lands on the beam over the north side of the platform. Next, I tilt the left stick directly up (I even look at the controller during this maneuver to fine-tune the direction of the left stick) and jump for a third time to land on the execution platform. I continue to hold the left stick up so that Altair rolls toward Majd Addin after landing. Then I press attack near the end of the roll to pounce on Majd Addin as he turns around.
As I mentioned previously, the timing of the jumping is critical. If you start a split second too early, Majd Addin will see you land on the beam on the north side of the platform. If you start a split second too late, he will see you land on the platform. In either case, you will become Exposed, and he will block your hidden blade attack if you bother to attempt one. After the first jump, I know I've timed it correctly if the Altair catches the ledge on the second syllable of "reject" in Majd Addin's speech.
The strict timing requirements are only necessary for this specific assassination design (Majd at the far south end of the platform, before the first victim dies). An easier mission design is to kill Majd Addin as he walks toward the "temptress." This simplified quadruple jump does not require any rolling after landing on the platform, and it is relatively easy to execute if you start the initial jump about 8 seconds earlier (timing is not critical).