Erla Porey Olafsdottir's sheep normally have two horns. On one ram, however, these appear to have fused into one, forking only a little at the end, thus matching the Latin origins of the word - uni and cornu - "single horn". To be doubly sure though, Erla's family have also named him Einhyrningur, "unicorn" in Icelandic.
The Iceland Monitor website reported that Einhyrningur was accidentally left on the mountainside when other sheep were rounded up for the winter. Farmers who spotted him at Christmas were not sure what he was at first, and thought he might be a goat.
"The horns stretch his face, particularly around the eyes so he always seems to be a bit surprised. He kind of looks like people that have had a facelift," Erla was quoted as saying.
The Ice News website reported that his owners did not rate him as a breeding sheep as he was "skinny", and had only planned to let him live till next spring. But the Iceland Monitor says that although a transfer to Reykjavik Zoo has been ruled out due to Iceland's strict rules on animal movements, he may still survive should another local farmer want to buy him.
Next story: Man lived above Japanese toilet for three years
Use #NewsfromElsewhere to stay up-to-date with our reports via Twitter.