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

Decoy state method for measurement device independent quantum key distribution with different intensities in only one basis