Demolition of the four-story Palmer Building in Harvard Square will begin November 1 to make way for expansion of both the Coop and the Harvard Trust Co., a Coop official said yesterday.

Bank authorities had previously announced the purchase of the office building, one of the oldest in the city, for the price of $300,000. The erection of a new four-story bank structure on the location will begin immediately after the razing.

J. G. Morrill, General Manager of the Coop, said the new building should be completed in the spring of 1957, when the Coop will take a 30-year lease on the bank's present floor offices.

Harvard Trust officials will decide next weekend whether they will plan a building of colonial design or a modernistic structure. The bank will keep the upstairs offices and the vaults in the basement of its present site.

Morrill said the Coop's program for expansion, which will not become effective until approximately the fall of 1957, is mainly to gain more selling space rather than make room for new goods.