  The magnetic flux periodicity of $\frac{hc}{2e}$ is a well known
manifestation of Cooper pairing in typical s-wave superconductors. In this
paper we theoretically show that the flux periodicity of a two-dimensional
second-order topological superconductor, which features zero-energy Majorana
modes localized at the corners of the sample, is $\frac{hc}{e}$ instead. We
further show that the periodicity changes back to $\frac{hc}{2e}$ at the
transition to a topologically trivial superconductor, where the Majorana modes
hybridize with the bulk states, demonstrating that the doubling of periodicity
is a manifestation of the non-trivial topology of the state.
