Context :

Aims : Our aim is to characterize the polarized continuum emission properties including intensity , polarization position angle , and polarization percentage of Sgr A* at \sim 492 GHz .
This frequency being well into the submillimeter-hump where the emission is supposed to become optically thin , allows us to see down to the event horizon .
Hence the reported observations contain potentially vital information on black hole properties .
We have compared our measurements with previous , lower frequency observations , which provides information in the time domain .

Methods : We report continuum emission properties of Sgr A* at \sim 492 GHz , based on the Atacama Large Millimeter Array ( ALMA ) observations .
We measured fluxes of Sgr A* from the central fields of our ALMA mosaic observations .
We used the observations of the likely unpolarized continuum emission of Titan , and the observations of C i line emission , to gauge the degree of spurious polarization .

Results : The flux of 3.6 \pm 0.72 Jy during our run is consistent with extrapolations from the previous , lower frequency observations .
We found that the continuum emission of Sgr A* at \sim 492 GHz shows large amplitude differences between the XX and the YY correlations .
The observed intensity ratio between the XX and YY correlations as a function of parallactic angle may be explained by a constant polarization position angle of \sim 158 ^ { \circ } \pm 3 ^ { \circ } .
The fitted polarization percentage of Sgr A* during our observational period is 14 % \pm 1.2 % .
The calibrator quasar J1744-3116 we observed at the same night can be fitted to Stokes I = 252 mJy , with 7.9 % \pm 0.9 % polarization in position angle P.A .
= 14.1 ^ { \circ } \pm 4.2 ^ { \circ } .

Conclusions : The observed polarization percentage and polarization position angle in the present work appear consistent with those expected from longer wavelength observations in the period of 1999-2005 .
In particular , the polarization position angle at 492 GHz , expected from the previously fitted 167 ^ { \circ } \pm 7 ^ { \circ } intrinsic polarization position angle and ( -5.6 \pm 0.7 ) \times 10 ^ { 5 } rotation measure , is 155 ^ { +9 } _ { -8 } , which is consistent with our new measurement of polarization position angle within 1 \sigma .
The polarization percentage and the polarization position angle may be varying over the period of our ALMA 12m Array observations , which demands further investigation with future polarization observations .