  We show that the three-intensity protocol for measurement device independent
quantum key distribution (MDI QKD) can be done with different light intensities
in {\em only one} basis. Given the fact that the exact values yields of
single-photon pairs in the $X$ and $Z$ bases must be the same, if we have lower
bound of the value in one basis, we can also use this as the lower bound in
another basis. Since in the existing set-up for MDI-QKD, the yield of sources
in different bases are normally different, therefore our method can improve the
key rate drastically if we choose to only use the lower bound of yield of
single-photon pairs in the advantageous basis. Moreover, since our proposal
here uses fewer intensities of light, the probability of intensity mismatch
will be smaller than the existing protocols do. This will further improve the
advantage of our method. The advantage of using Z basis or X basis of our
method is studied and significant improvement of key rates are numerically
demonstrated.
