The four-storey brick structure was the last of four buildings to be bowled over on the corner of Howick and Charles streets as part of a $5.169 million demolition project.

Heavy machinery has been on site since late January, and workers have knocked over the bulk of the Anne O'Byrne building since March.

The entire site is expected to be cleared and remediated by July.

A Department of Health spokesperson said the structure had been decommissioned in October after "reaching the end of its useful life".

"Future use of land and buildings in the LGH Precinct, including the Anne O'Byrne building, was considered in the development of the LGH Precinct Masterplan," the spokesperson said.

"The Department is continuing to prepare the site for future development."

The site had been set to welcome a $120 million private hospital under a partnership between Calvary Health Care and the state government.

The proposed facility was set to ease the demand on the neighbouring Launceston General Hospital and had been expected to open in 2026.

However, Calvary announced in February it would no longer go ahead with the project, citing cost blowouts.

"Our team has invested an enormous amount of time and energy to try and deliver the co-located private hospital, however, the associated challenging budget escalations are insurmountable for Calvary at this time," national chief executive Martin Bowles said.

A replacement partner for Calvary is yet to be locked in.

However, Health Minister Guy Barnett has said the state government remains determined to deliver a new private hospital at the site.

"I want to make it abundantly clear our government remains committed to partnering with providers to see this project through," he said in February.

"That's why we are progressing with the demolition of a number of buildings at the LGH, some of which date back to the 1960s and '80s, to make way for a co-located private hospital.

"We are continuing to roll out our LGH Masterplan."

The Anne O'Byrne building may be gone, but its namesake - who served many health, women's and political boards between the 1960s and 1990s - is still recognised in the precinct.

Level one of the new tunapri mapali building on the corner of Frankland and Charles streets was named the Anne O'Byrne Education Centre in late 2022.