PSR B1259-63/LS 2883 is a binary system consisting of a 48 ms pulsar orbitting around the Be star with an orbital period of 3.4 years. The system was detected at very high energies (VHE; E>100 GeV) by the High Energy Stereoscopic System (H.E.S.S.) during its periastron passages in 2004 and 2007. New H.E.S.S. observations of the source taken from 9th to 16th of January 2011, i.e., 25-32 days after the most recent periastron passage of the system on December 15th 2010 are presented here. These new observations partially overlap with the beginning of a spectacular gamma-ray flare reported by the Fermi-LAT. H.E.S.S. detects the source at a high significance level in this time range without signatures of the emission enhancement. H.E.S.S. results show both flux and spectral properties similar to those reported in previous periastron passages. A careful statistical study based on the Fermi and H.E.S.S. lightcurves lead to the conclusion that GeV and TeV emission have a different physical origin. The GeV emission is used then to constrain the electron population responsible for the TeV emission in the leptonic scenario.