Dr Skinner descended first and, after finding a steep icy section, stopped to place an anchor to secure further descent.
Ms Martin - some 15m behind him - then slipped and yelled as she went past him, trying to halt her rapid descent by using her crampons.
While trying to hold the impact with his rope, Dr Skinner was pulled from his position and they both plummeted down the steep ice.
He was knocked out in the fall, and when he awoke found his partner some 20m above him, lodged in a small crevasse which had stopped her fall.
She was not moving and he could not find a pulse, and activated a locater beacon while giving her first aid.
A search and rescue volunteer was winched to the scene by helicopter and found Ms Martin dead at the scene.
A post mortem examination found the cause of death was diffuse cerebral injury from blunt force impact.
A report on the fall for Otago/Southland coroner David Crerar was provided by experienced mountain guide and climber Murray Cullen, who concluded the surface at the site was largely hard brittle ice and the slope of the glacier less than 30 degrees.
The couple should have used the "American technique'', where climbers turn sideways on steep slopes using a step-through technique, and the "front-pointing technique'' on brief sections when the slope steepened, he said.
Mr Cullen said the only snow anchor mentioned by Dr Skinner was a snow stake, which would not have been appropriate given the icy conditions.
When descending, the strongest climber should take the upper position, and Dr Skinner should have been the rear climber as he was the stronger and more confident of the two.
That Ms Martin felt uneasy was a warning signal that a fixed belay was appropriate.
The coroner said the ascent and descent of the glacier was not beyond the couple's experience.
But her death "is a timely reminder to all visitors to the New Zealand mountains that the environment is hazardous, that no shortcuts in appropriate techniques can be taken, and that absolute care and concentration is essential at all times''.