  Ringdown gravitational waves of compact object binaries observed by
ground-based gravitational-wave detectors encapsulate rich information to
understand remnant objects after the merger and to test general relativity in
the strong field. In this work, we investigate the ringdown gravitational waves
in detail to better understand their property, assuming that the remnant
objects are black holes. For this purpose, we perform numerical simulations of
post-merger phase of binary black holes by using the black hole perturbation
scheme with the initial data given under the close-limit approximation, and
generate data of ringdown gravitational waves with smaller numerical errors
than that associated with currently available numerical relativity simulations.
Based on the analysis of the data, we propose an orthonormalization of the
quasinormal mode functions describing the fundamental tone and overtones to
model ringdown gravitational waves. Finally, through some demonstrations of the
proposed model, we briefly discuss the prospects for ringdown
gravitational-wave data analysis including the overtones of quasinormal modes.
