The Special Beam Kamehameha was the product of Ukele's training of Cell (clone) during the Ukele Saga.
Ukele created Cell (clone) to help take down the Z Fighters. During his life, he observed the Z Fighters and learned some of the Special Beam Cannon technique from observing Piccolo. This lead to Ukele creating the Special Beam Blast.
Utilizing his knowledge of Cell's makeup (including the DNA of several Kamehameha users as well as Piccolo's and being able to perform both moves) and Ukele's own experience developing the Special Beam charging technique, he and Cell were able to create a new move.
By charging an attack using the Special Beam method by placing one hand on the forehead and focusing the energy, and then moving into Kamehameha position immediately afterwards and charging a Kamehameha, a new attack could be created. The result was the Special Beam Kamehameha. It looks exactly like a Kamehameha, but with spirals surrounding it as it fires, just like with the Special Beam Cannon.
The strength is incredible and it is fast in firing. Either stage can be held for more charging, and saying the name of the attack, while not needed, appears to increase the power while charging. Cell (clone) is the only known user of the attack.