We present results of a survey of Lyα emitters (LAEs) at z= 6.5 which is thought to be the final epoch of the cosmic re-ionization. In a ≈530 arcmin2 deep image of the SSA22 field taken through a narrow-band filter NB912 installed in the Subaru/Suprime-Cam, we have found only 14 LAE candidates with LLyα≳ 3 × 1042 erg s−1. Even applying the same colour selection criteria, the number density of the LAE candidates is a factor of 3 smaller than that found at the same redshift in the Subaru Deep Field (SDF). Assuming the number density in the SDF is a cosmic average, the probability to have a number density equal to or smaller than that found in the SSA22 field is only 7 per cent if we consider fluctuation by the large-scale structure (i.e. cosmic variance) and Poisson error. Therefore, the SSA22 field may be a rare void at z= 6.5. On the other hand, we have found that the number density of i′-drop galaxies with 25.5 < z′ < 26.0 in the SSA22 field agrees well with that in the SDF. If we consider a scenario that a larger neutral fraction of intergalactic hydrogen, xH I, in the SSA22 field obscures a part of Lyα emission, xH I in the SSA22 field should be about two times larger than that in the SDF. This can be translated into xH I < 0.9 at z= 6.5 in the SSA22 field. A much larger survey area than previous ones is required to overcome a large fluctuation reported here and to obtain a robust constraint on xH I at the end of the re-ionization from LAEs.