A new type of neutrino mixing named bi-pair neutrino mixing is proposed to describe the current neutrino mixing pattern with a vanishing reactor mixing angle and is determined by a mixing matrix with two pairs of identical magnitudes of matrix elements. As a result, we predict \sin^2θ_{12}=1-1/\sqrt{2}(\approx 0.293) for the solar neutrino mixing and either \sin^2θ_{23}=\tan^2θ_{12} or \cos^2θ_{23}=\tan^2θ_{12} for the atmospheric neutrino mixing. We determine flavor structure of a mass matrix M, leading to diagonal masses of m_{1,2,3}, and find that |M_{μμ}-M_{ee}/t^2_{12}|:|M_{μτ}|:|M_{ττ}-M_{ee}/t^2_{12}|=t^2_{23}:|t_{23}|:1 for the normal mass hierarchy if m_1=0, where t_{ij}=\tanθ_{ij} (i,j=1,2,3) and M_{ij} (i,j=e,μ,τ) stand for flavor neutrino masses. For the inverted mass hierarchy, the bi-pair mixing scheme turns out to satisfy the strong scaling ansatz requiring that |M_{μμ}|:|M_{μτ}|:|M_{ττ}|=1:|t_{23}|:t^2_{23} if m_3=0.

4 pages, version accepted for publication of Physics Letters B