  A new class of Weyl invariant backgrounds are presented in terms of the
metric $G_{\mu\nu}$ and the anti-symmetric Kalb-Ramond fields $B_{\mu\nu}$. The
ten-dimensional spacetime is a product of four-dimensional flat spacetime and
curved six-dimensional spacetime having nonvanishing Ricci tensors. The
non-vanishing Kalb-Ramond field strengths cannot be written globally as $H=dB$,
being of the monopole type. Nevertheless they define homogeneous spacetime with
no singularity.
