For a finite dimensional CW-complex, X, and
q
>
1
q > 1
, it is shown that the qth Čech cohomology group based on finite open covers of X,
H
f
q
(
X
)
H_f^q(X)
, is naturally isomorphic to
H
q
(
X
)
{H^q}(X)
, the qth Čech cohomology of X (i.e. based on locally finite covers), and for reasonable X,
H
1
(
X
)
{H^1}(X)
can be obtained algebraically from
H
f
1
(
X
)
H_f^1(X)
.