  Let a real-analytic manifold $M$ formally (holomorphically) equivalent to the
following model
\begin{equation*}w=z_{1}\overline{z}_{1}+\dots+z_{N}\overline{z}_{N}+\lambda_{1}\left(z_{1}^{2}+\overline{z}_{1}^{2}\right)+\dots+\lambda_{N}\left(z_{N}^{2}+\overline{z}_{N}^{2}\right),{equation*}
assuming that $$ \lambda_{1},\dots, \lambda_{N}\in
\left[0,\frac{1}{2}\right).$$ It is proven that $M$ is holomorphically
equivalent to this model by developing a partial normal form for such
real-analytic submanifold using generalized Fischer Decompositions. In
particular, there are defined certain Spaces of Normalizations used also in
proving other analogues of The Theorem of Moser in certain non-equidimensional
situations. There presented also other applications for the methods considered.
