An excess observed in the accelerator neutrino experiments in the
channel at high confidence level (CL) has been interpreted as due to eV-scale sterile neutrino(s). But, it has been suffered from the problem of ``appearance - disappearance tension'' at the similarly high CL because the measurements of the
channel do not observe the expected event number depletion corresponding to the sterile contribution in the appearance channel. We suggest non-unitarity as a simple and natural way of resolving the tension, which leads us to construct the non-unitary
(3+1) model. With reasonable estimation of the parameters governing non-unitarity, we perform an illustrative analysis to know if the tension is resolved in this model. At the best fit of the appearance signature we have found the unique solution with
, which is consistent with the (reactors + Ga) data combined fit. Unexpectedly, our tension-easing mechanism bridges between the two high CL signatures, the BEST and LSND-MiniBooNE anomalies.