He was on the second floor of the building when the first quake struck and the roof caved in.
Some staff tried to leave the building through a back stairwell but it was filled with dust.
They managed to get down the main stairwell, he said.
''There was debris everywhere.''
Just as they got out of the building a strong aftershock struck.
''The front of the building just fell off on to the street in front of us.''
Mr Conway, a senior reporter with The Press, received cuts to his head, and scratches, but was not otherwise hurt ''apart from a headache and being covered in dust and blood''.
He believed five staff from the finance department were trapped in the building, although one had got out.
It was very hard to balance his job as a journalist with concern for family and friends, he said.
While his family was safe, at least one colleague had possibly lost a family member and he was aware they would probably know many of those who died.
''It'll hit us at some stage but we're going to make an effort to try and get as much out from today and tomorrow as possible.''
The Press was setting up a newsroom at its new press building outside the central city.
Another former Otago Daily Times reporter, Lee Harris, said she was in her office in Madras St, in the central business district, when the quake struck.
Everyone dived under the doorways until it stopped and when they looked out the window they saw the building next door had collapsed, with rubble squashing cars in the street.
''People were hugging other people - random strangers.''
She then spent more than two hours trying to get out of the city to her suburban Barrington home as many roads and bridges were closed or blocked.
''A lot of buildings have come down - it seems mostly those which were affected badly the first time around.''
Her daughter, who worked for the Earthquake Commission, got out of its office building which was damaged, she said.
The experience after September's earthquake showed the city could recover.
''We know we can come back - we did last time.''
