  We propose a novel recursive way of updating the tensors in projected
entangled pair states by evolving the tensor in imaginary time evolution on
clusters of different sizes. This generalizes the so- called simple update
method of Jiang et al. [Phys. Rev. Lett. 101, 090603 (2008)] and the updating
schemes in the single layer picture of Pi\v{z}orn et al. [Phys. Rev. A 83,
052321 (2011)]. A finite-size scaling of the observables as a function of the
cluster size provides a remarkable improvement in the accuracy as compared to
the simple update scheme. We benchmark our results on the hand of the spin 1/2
staggered dimerized antiferromagnetic model on the square lattice, and accurate
results for the magnetization and the critical exponents are determined.
