  We found an universal local unitary (orthogonal) transformation which
transforms any centrosymmetric (CS) density matrix \rho_{CS} into the X density
matrix \rho_X: H\otimes H\rho_{CS}H\otimes H=\rho_X, where H is the Hadamard
transformation. Because quantum discord is invariant under the local unitary
transformations, this remarkable property allows to get the discord of general
two-qubit CS states in the analytical form using the corresponding well-known
formulas for the X states. Examples of systems with CS density matrices
provided from the recent literature, including XXZ spin model with the
Dzyaloshinsky-Moriya interaction, a gas of spin-carrying particles in closed
nanopore, and a family of pseudopure states.
