Detectives are trying to establish a motive for why a devoted husband and father would kill his "perfect family" before taking his own life.
Richard Smith is thought to have killed his wife Clair and their children Ben, nine, and Aaron, one, before taking his own life at the home they shared in Pudsey, near Leeds.
Police have launched a murder inquiry, but have said they are not looking for anyone else, after the bodies were found in a fire-damaged upstairs bedroom on Sunday afternoon.
Mr Smith, 37, who worked for a shopfitting firm, and his 36-year-old wife are thought to have moved into the modern stone-built house a few months ago.
The tragedy appears to be another incident involving a father killing his family. It is thought there is no obvious motive for Smith's actions.
The bodies were removed from the house and taken away in a private ambulance. Officers are trying to establish how each family member died.
Relatives and neighbours spoke of their shock as news of the killings became public.
Family friend Sara Turnbull was in tears as she left flowers at the police cordon.
The message on her bouquet said: "You were such a beautiful family. All our love to you. We can't believe you are all gone."
Her husband Dean said the families had known each other for 15 years and been on a number of holidays together.
