  Tate first proposed a method to determine $K_2\mathcal{O}_F,$ the tame kernel
of $F,$ and gave the concrete computations for some special quadratic fields
with small discriminant. After that, many examples for quadratic fields with
larger discriminants are given, and similar works also have been done for cubic
fields and for some special quartic fields with discriminants not large. In the
present paper, we investigate the case of more general imaginary cyclic quartic
field $F=\mathbb{Q}\Big(\sqrt{-(D+B\sqrt{D})}\Big)$ with class number one and
large discriminants. The key problem is how to decrease the huge theoretical
bound appearing in the computation to a manageable one and the main difficulty
is how to deal with the large-scale data emerged in the process of computation.
  To solve this problem we have established a general architecture for the
computation, in particular we have done the works:
  (1) the PARI's functions are invoked in C++ codes;
  (2) the parallel programming approach is used in C++ codes;
  (3) in the design of algorithms and codes, the object-oriented viewpoint is
used, so an extensible program is obtained.
  As an application of our program, we prove that $K_2\mathcal{O}_F$ is trivial
  in the following three cases: $B=1,D=2$ or $B=2, D=13$ or $B=2, D=29.$
  In the last case, the discriminant of $F$ is 24389, hence, we can claim that
our architecture also works for the computation of the tame kernel of a number
field with discriminant less than 25000.
