In this paper, we consider the fractional critical Schrödinger equation (FCSE) $$(-\Delta)^su-|u|^{2^*_s-2}u=0,$$ where $u∈\dot{H}^s(\mathbb{R}^N),$ $N≥4,$ $0<s<1$ and $2^∗_s=\frac{2N}{N−2s}$ is the critical Sobolev exponent of order $s.$ By virtue of the variational method and the concentration compactness principle with the equivariant group action, we obtain some new type of nonradial, sign-changing solutions of (FCSE) in the energy space $\dot{H}^s(\mathbb{R}^N)$. The key component is that we take the equivariant group action to construct several subspace of $\dot{H}^s(\mathbb{R}^N)$ with trivial intersection, then combine the concentration compactness argument in the Sobolev space with fractional order to show the compactness property of Palais-Smale sequences in each subspace and obtain the multiple solutions of (FCSE) in $\dot{H}^s(\mathbb{R}^N).$
