  We have studied the edge spin accumulation in a high mobility two-dimensional
electron gas formed in a symmetric well with two subbands. This study is
strongly motivated by the recent experiment of Hernandez et al. [Phys. Rev. B
{\bf 88}, 161305(R) (2013)] who demonstrated the spin accumulation near the
edges of a bilayer symmetric GaAs structure in contrast to no effect in a
single-layer configuration. The intrinsic mechanism of the spin-orbit
interaction we consider arises from the coupling between two subband states of
opposite parities. We obtain a parametrically large magnitude of the edge spin
density for the two-subband sample as compared to the usual single-subband
structure. We show that the presence of a gap in the system, i.e., the energy
separation $\Delta$ between the two subband bottoms, changes drastically the
picture of the edge spin accumulation. Thus one can easily proceed from the
regime of weak spin accumulation to the regime of strong one by varying the
Fermi energy (electron density) and/or $\Delta$. We estimate that by changing
the gap $\Delta$ from zero up to $1\div 2$ K, the magnitude of the effect
changes by three orders of magnitude. This opens up the possibility for the
design of new spintronic devices.
