  We propose an indirect approach to the generation of a two-dimensional
quasiperiodic (QP) pattern in convection and similar nonlinear dissipative
systems where a direct generation of stable uniform QP planforms is not
possible. An {\it eightfold} QP pattern can be created as a broad transient
layer between two domains filled by square cells (SC) oriented under the angle
of 45 degrees relative to each other. A simplest particular type of the
transient layer is considered in detail. The structure of the pattern is
described in terms of a system of coupled real Ginzburg-Landau (GL) equations,
which are solved by means of combined numerical and analytical methods. It is
found that the transient ``quasicrystallic'' pattern exists exactly in a
parametric region in which the uniform SC pattern is stable. In fact, the
transient layer consists of two different sublayers, with a narrow additional
one between them. The width of one sublayer (which locally looks like the
eightfold QP pattern) is large, while the other sublayer (that seems like a
pattern having a quasiperiodicity only in one spatial direction) has a width
$\sim 1$. Similarly, a broad stripe of a {\it % twelvefold} QP pattern can be
generated as a transient region between two domains of hexagonal cells oriented
at the angle of 30 degrees.
