  In \cite{Lei}, the author derived an exact rotation-strain model in two
dimensions for the motion of incompressible viscoelastic materials via the
polar decomposition of the deformation tensor. Based on the rotation-strain
model, the author constructed a family of large global classical solutions for
the 2D incompressible viscoelasticity. To get such a global well-posedness
result, the equation for the rotation angle was essential to explore the
underlying weak dissipative structure of the whole viscoelastic system even
though the momentum equation for the velocity field and the transport equation
for the strain tensor have already formed a closed subsystem. In this paper, we
revisit such a result without making use of the equation of the rotation angle.
The proof relies on a new identity satisfied by the strain matrix. The
smallness assumptions are only imposed on the $H^2$ norm of initial velocity
field and the initial strain matrix, which implies that the deformation tensor
is allowed being away from the equilibrium of 2 in the maximum norm.
