Any imaginary cyclic quartic field can be expressed uniquely in the form
K
=
Q
(
A
(
D
+
B
D
)
)
K = Q(\sqrt {A(D + B\sqrt D )} )
, where A is squarefree, odd and negative,
D
=
B
2
+
C
2
D = {B^2} + {C^2}
is squarefree,
B
>
0
,
C
>
0
B > 0,C > 0
, and
(
A
,
D
)
=
1
(A,D) = 1
. Explicit formulae for the discriminant and conductor of K are given in terms of A, B, C, D. The calculation of tables of the class numbers
h
(
K
)
h(K)
of such fields K is described.