  We propose a systematic way of constructing Floquet second-order topological
insulators (SOTIs) based on time-glide symmetry, a nonsymmorphic space-time
symmetry that is unique in Floquet systems. In particular, we are able to show
that the static enlarged Hamiltonian in the frequency domain acquires the
reflection symmetry, which is inherited from the time-glide symmetry of the
original system. As a consequence, one can construct a variety of time-glide
symmetric Floquet SOTIs using the knowledge of static SOTIs. Moreover, the
time-glide symmetry only needs to be implemented approximately in practice,
enhancing the prospects of experimental realizations. We consider two examples,
a 2D system in class AIII and a 3D system in class A, to illustrate our ideas,
and then present a general recipe for constructing Floquet SOTIs in all
symmetry classes.
