  We give a simple example of spacetime metric, illustrating that homogeneity
and isotropy of space slices at all moments of time is not obligatory lifted to
a full system of six Killing vector fields in spacetime, thus it cannot be
interpreted as a symmetry of a four dimensional metric. The metric depends on
two arbitrary and independent functions of time. One of these functions is the
usual scale factor. The second function cannot be removed by coordinate
transformations. We prove that it must be equal to zero, if the metric
satisfies Einstein's equations and the matter energy momentum tensor is
homogeneous and isotropic. A new, equivalent, definition of homogeneous and
isotropic spacetime is given.
