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Project managers say the redevelopment is on time and on budget for its opening on February 5.
The Government agreed to save the ailing building in 2015, after Dunedin City Council lobbying, petitions and community pressure.
The Stuart St facility was closed in 2011 and a temporary facility established in High St after engineers found parts of the building fell short of the minimum 34% rating required under the National Building Standard.
Project manager Jeff Halmshaw showed Courts Minister Amy Adams around the building yesterday.
Mrs Adams is in Dunedin on a campaign visit, announcing funding for a youth facility.
The interior of the building is still a building site. Electrical wiring pokes from ceilings and plywood covers interior items.
Mr Halmshaw and project manager Kevin Long told Mrs Adams about piles that had been injected 14m into the ground to displace "useless" earth on the site that used to be the harbour foreshore.
Steel bands to strengthen the building were bolted to the walls.
External features are also now bolted on.
Contractors had so far replaced 73 of 106 leadlight windows, the older versions damaged when stone on the building was cleaned in the 1990s.
An existing window would be mounted and put on display.
The main Stuart St entrance would no longer be used for public access, because of issues providing disability access.
Mr Halmshaw promised "no surprises" that would delay the upgrade.
Mrs Adams described the progress of the upgrade as "really encouraging".
She said there had been no requests for funding above the budget.