Rosh Ĥodesh is a time of atonement, as we recite in the Musaf prayer, "a time of atonement for all their offspring." In addition, in the time of the Temple, a male goat would be brought as a sin offering.

In order to make this atonement complete, pious Jews customarily repent in for the time leading up to Rosh Ĥodesh. Some people fast on the day before Rosh Ĥodesh and recite special Yom Kippur Katan prayers prior to the Minĥa service. The day before Rosh Ĥodesh is called Yom Kippur Katan ("the minor Yom Kippur") because it is a time to atone for the sins of the previous month, just as Yom Kippur is a time to atone for the sins of the previous year (see mb 417:4, Kaf Ha-ĥayim 417:10-21). Nowadays, few people follow the custom of fasting; instead of fasting, one can study more Torah and give extra charity.