2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132930Based on the Orlov and Shulman's M operator, the additional symmetries and the string equation of the CKP hierarchy are established, and then the higher order constraints on $L^l$ are obtained. In addition, the generating function and some properties are also given. In particular, the additional symmetry flows form a new infinite dimensional algebra $W^C_{1+\infty}$, which is a subalgebra of $W_{1+\infty}$.13pages, LaTex, to appear in Lett.Math.PhysExactly Solvable and Integrable Systemstext