  We report a detailed analysis of the orbital properties of binary millisecond
pulsar (MSP) with a white dwarf (WD) companion. Positive correlations between
the orbital period $P_{\rm b}$ and eccentricity $\epsilon$ are found in two
classes of MSP binaries with a He WD and with a CO/ONeMg WD, though their
trends are different. The distribution of $P_{\rm b}$ is not uniform.
Deficiency of sources at $P_{\rm b}\sim35-50$~days (Gap 1) have been mentioned
in previous studies. On the other hand, another gap at $P_{\rm
b}\sim2.5-4.5$~days (Gap 2) is identified for the first time. Inspection of the
relation between $P_{\rm b}$ and the companion masses $M_{\rm c}$ revealed the
subpopulations of MSP binaries with a He WD separated by Gap 1, above which
$P_{\rm b}$ is independent of $M_{\rm c}$ (horizontal branch) but below which
$P_{\rm b}$ correlates strongly with $M_{\rm c}$ (lower branch). Distinctive
horizontal branch and lower branch separated by Gap 2 were identified for the
MSP binaries with a CO/ONeMg WD at shorter $P_{\rm b}$ and higher $M_{\rm c}$.
Generally, $M_{\rm c}$ are higher in the horizontal branch than in the lower
branch for the MSP binaries with a He WD. These properties can be explained in
terms of a binary orbital evolution scenario in which the WD companion was
ablated by a pulsar wind in the post mass-transfer phase.
