  Based 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 $W_{1+\infty}$.
