Generalizing the involution length of the complex hyperbolic plane, we obtain that the α-length of $\mathrm{PU}(2,1)$ is 4, that is, every element of $\mathrm{PU}(2,1)$ can be decomposed as the product of at most four special elliptic isometries with parameter α. We also describe the isometries that can be written as the product of two or three such special elliptic isometries.