  The discrete single-particle spectra in both the Fermi and Dirac sea have
been calculated by the imaginary time step (ITS) method for the
Schr\"{o}dinger-like equation after avoiding the "tsunami" of the Dirac sea,
i.e., the diving behavior of the single-particle level into the Dirac sea in
the direct application of the ITS method for the Dirac equation. It is found
that by the transform from the Dirac equation to the Schr\"{o}dinger-like
equation, the single-particle spectra, which extend from the positive to the
negative infinity, can be separately obtained by the ITS evolution in either
the Fermi sea or the Dirac sea. Identical results with those in the
conventional shooting method have been obtained via the ITS evolution for the
equivalent Schr\"{o}dinger-like equation, which demonstrates the feasibility,
practicality and reliability of the present algorithm and dispels the doubts on
the ITS method in the relativistic system.
