Let L be a finite dimensional Lie algebra. A subalgebra H of L is called a c^{#}-ideal of L, if there is an ideal K of L with L=H+K and Hcap K is a CAP-subalgebra of L. This is analogous to the concept of a c^{#}-normal subgroup of a finite group. Now, we consider the influence of this concept on the structure of finite dimentional Lie algebras.