In traditional materials science, structural disorder tends to break the symmetry of the lattice. In this work, however, we studied a case which may be opposite to this intuition. The prototypical phase change material, GeTe, undergoes the phase transition from the rhombohedral structure to a more symmetric cubic one at $625 K. Using ab initio molecular dynamics simulations, we demonstrated that even in the cubic phase, the lattice is constructed by random short and long bonds, instead of bonds with a uniform length.Such bifurcation of the bond lengths enabled by Peierls-like distortion persists in the entire temperature range (0-900 K), yet with different degrees of disorder, e.g., the atoms are distorted along a certain direction in the rhombohedral phase (i.e., structural order) but the distortion varies stochastically in terms of direction and amplitude at high T (i.e., structural disorder). A more symmetric lattice frame coexisting with severe local structural disorder is the signature of this cubic GeTe. Our simulations have provided a theoretical support on the disordered Peierls-like distortion in the high-T cubic phase discovered earlier by X-ray experiments. By modulating the physical properties that different degrees of disorder may induce, we are able to design better functional materials for various applications in electronic and photonic devices.