Its custodians, the Church Property Trustees, released three design options for a future cathedral earlier this year.
It included restoration, a timber replacement, or a contemporary design - which the Church says it prefers.
Asked if the Church will go ahead with the demolition, Bishop Matthews refused to comment until she'd met lawyers.
The Church's plan to deconstruct the damaged building to a "safe level'' of 2-3 metres above the ground, prompted public protests and the Great Christchurch Buildings Trust (GCBT), led by former MP Jim Anderton, went to the High Court to reverse the move.
Justice Lester Chisholm ruled the Church was entitled to deconstruct the damaged 132-year-old cathedral, but only if a new one was built on the same city centre site.
The GCBT challenged the decision in the Court of Appeal, which today released a judgement unanimously upholding the High Court's findings.
It means the Church is now entitled to continue deconstructing the building, but not until the High Court settles a number of outstanding issues, including whether the Church will repay an insurance payout used to build its temporary 'cardboard' cathedral.
The GCBT said it was "very disappointed'' with the decision, but has not given up hope.
Spokesman Mr Anderton told APNZ they'll be meeting with their legal advisers over the next week to decide what options are left open to them.
"We don't want to make a kneejerk reaction - these things have to be considered carefully,'' he said.
"The Church has been given the right by the Court of Appeal to, in the end, pull down the building.
"Whether that's the right decision for the city is of course one for people to make up their minds on - it's obviously one we don't agree with.''
The cathedral, designed by English Gothic designer George Gilbert Scott, was consecrated on November 1, 1881.
It withstood violent earthquakes in 1881, 1888, 1922, 1901 and on September 4, 2010.
Christchurch mayor Bob Parker said although the courts' decision will split public opinion, he welcomed the sense of finality it brings.
"It's time to let it go, and to let the Church get on with creating something positive in the heart of our city.''