Henry Claude Killender was born in Liverpool, Lancashire, England on 5 June 1892. In the 1911 England and Wales Census his occupation is given as Architect's Apprentice, however, it is not known where or with whom he trained. By the early 1920s he had qualified as an architect and was in partnership with Arthur Cecil Townsend (1896-1993) in Liverpool. They submitted a design for a bungalow in the Daily Mail Architects Competition for Labour-Saving Bungalows in 1922.
Killender was elected an Associate of the Royal Institute of British Architects (ARIBA) in 1922. His address was given as Jubilee Buildings, 16, Lord Street, Liverpool in 1922; Imperial Chambers, 62 Dale Street, Liverpool in 1926 and 1939. He died in Birkenhead, Cheshire in 1976