  A class of transformations of $R_q$-matrices is introduced such that the
$q\to 1$ limit gives explicit nonstandard $R_{h}$-matrices. The transformation
matrix is singular itself at $q\to 1$ limit. For the transformed matrix, the
singularities, however, cancel yielding a well-defined construction. Our method
can be implemented systematically for R-matrices of all dimensions and not only
for $sl(2)$ but also for algebras of higher dimensions. Explicit constructions
are presented starting with ${\cal U}_q(sl(2))$ and ${\cal U}_q(sl(3))$, while
choosing $R_q$ for (fund. rep.)$\otimes$(arbitrary irrep.). The treatment for
the general case and various perspectives are indicated. Our method yields
nonstandard deformations along with a nonlinear map of the $h$-Borel subalgebra
on the corresponding classical Borel subalgebra. For ${\cal U}_h(sl(2))$ this
map is extended to the whole algebra and compared with another one proposed by
us previously.
