The new church in Kunoy began construction on May 20, 1867, and was completed by October 17, 1867, according to the records preserved in historical documents. The church was built by local carpenters from Kunoy. The wood used was carefully selected, with no defect smaller than one and a half inches. Símun from Suðuri in Haraldssund served as the leader of the building project, and he also crafted the pulpit, the frames, and the windows. Notably, Símun had previously overseen the construction of the Klaksvík church around the same time.

The church initially lacked an altar piece and a chandelier. Kunoy residents, who were fishermen, provided fish for these items, and Faktor Djurhuus in Klaksvík was tasked with acquiring both the altar piece and the chandelier for the church.

The church was consecrated on December 1, 1867, by the parish priest Ernst Bugislaus Wesenberg, on the first Sunday of Advent.

According to Kirkesyn på Færøerne 1834-1884, a church inspection held on July 14, 1868, described the church as 22 alen (about 12 meters) long and 11 alen (about 6 meters) wide, with a slate roof, an arched ceiling, and painted interiors both inside and out, making it spacious and elegantly designed.

In April 13, 1992, the Government of the Faroe Islands declared the church and its churchyard to be protected as a historical monument, though they remain in use for their intended religious purposes.

(Source: J.P. Gregoriussen, “Eldru Hválvkirkjurnar”)