  The density of states modulation recently observed by the scanning tunneling
microscopic experiment in the pseudogap state of high-$T_c$ superconductors is
explained by the pairing assisted particle transitions under perturbation of a
periodic pairing interaction. In such a transition process, a particle with
momentum ${\bf k}$ firstly picks up another particle of inverse spin to produce
a pair leaving a hole. Under the perturbation of periodic pairing interaction
of modulation wave vector ${\bf Q}$, the pair absorbs a momentum ${\bf Q}$ and
then breaks into two single-particles: one propagates with momentum ${\bf
k+Q}$, and another one fills in the hole. The transition is significant at low
energies within the pseudogap since where the pairing excitations most
favorably survive. We calculate the Fourier component of the modulated density
of states using two different models. Both of the theoretical results are
consistent with the experiment.
