  We present a result of a blind search for [CII] 158 $\mu$m emitters at $z\sim
4.5$ using ALMA Cycle~0 archival data. We collected extra-galactic data
covering at 330-360 GHz (band~7) from 8 Cycle~0 projects from which initial
results have been already published. The total number of fields is 243 and the
total on-source exposure time is 19.2 hours. We searched for line emitters in
continuum-subtracted data cubes with spectral resolutions of 50, 100, 300 and
500 km/s. We could not detect any new line emitters above a 6-$\sigma$
significance level. This result provides upper limits to the [CII] luminosity
function at $z\sim 4.5$ over $L_{\rm [CII]} \sim 10^8 - 10^{10} L_{\odot}$ or
star formation rate, SFR $\sim$ 10-1000 M$_{^\odot}$/yr. These limits are at
least 2 orders of magnitude larger than the [CII] luminosity functions expected
from the $z \sim 4$ UV luminosity function or from numerical simulation.
However, this study demonstrates that we would be able to better constrain the
[CII] luminosity function and to investigate possible contributions from dusty
galaxies to the cosmic star-formation rate density by collecting Cycle~1+2
archival data as the ALMA Patchy Deep Survey.
