  Let $X$ be an Abelian cover $\mathbb{CP}^{1}$ ramified at $mr$ points,
$\lambda_1...\lambda_{mr}.$ we define a class of non positive divisors on $X$
of degree $g-1$ supported in the pre images of the branch points on $X$, such
that the Riemann theta function doesn't vanish on their image in $J(X).$ We
obtain a Thomae formula similar to the formulas [BR],[Na],[Z] ,[EG] and [Ko].
We show that up to a certain determinant of the non standard periods of $X$,
the value of the Riemann theta function at these divisors raised to a high
enough power is a polynomial in the branch point of the curve $X.$ Our approach
is based on a refinement of Accola's results and Nakayashiki's approach
explained in [Na] for Abelian covers.
