Half of the 10 'supergeese' being tracked on their migration have been killed or are missing.
The journey of the geese is being tracked by the WWT
The Brent geese are being monitored on their journey from Ireland to Greenland by the Wildfowl and Wetlands Trust.
The WWT said they had learnt one of them, Douglas, had been shot by a hunter, who returned the transmitter, along with the bird's legs.
The progress of the rest can be followed at www.wwt.org.uk/supergoose and www.bbc.co.uk/autumnwatch.
The WWT said that this week that 'supergoose' Arthur had also been reported missing.
Ten 'supergeese' were fitted with transmitters by WWT scientists in the spring. Now only five - Orville, Howard, Alberto, Clark Brent and Hermes - can still be tracked.
Douglas met his demise on Disco Bay, Western Greenland, when hunters were reported to have seen a group of seven light-bellied Brent Geese and shot and killed two of them - one of them Douglas.
When the hunter discovered the WWT satellite transmitter he reported it and returned the transmitter complete with Douglas' severed legs and leg rings so the goose could be identified.
The return journey from the Arctic Tundra, over the Greenland ice-cap through Iceland and back to Ireland is fraught with hazards and illegal hunting is just one of the obstacles that the migrating geese must face every year.
WWT project scientist Kendrew Colhoun, said other birds may also have been killed.
"While we can't be sure of the precise reasons why some of the tracked geese have disappeared, Douglas's fate may well have been shared by others," he said.
"It is unlikely that all birds have been shot as other reasons may be responsible including mortality due to poor weather or transmitter malfunction, or loss, are also possible.
"What happened to Douglas is however illustrative of one of the many hazards these birds face on this long and arduous migration.
"Finding out this sort of information on mortality sources, identifying migratory routes and the importance of staging areas are key objectives of the project."
He added that he hoped the death of Douglas will help the WWT to argue for stricter conservation measures of this population as they pass through Greenland in spring and autumn.
Light-bellied Brent geese are a protected species in the UK, Ireland, Iceland and Greenland.
The return of Supergoose will feature on BBC Autumnwatch with Bill Oddie during the first two weeks of October (Monday - Thursday evenings on BBC Two at 2000 BST starting 2 October).