Did unicorns exist in ancient times?

A Southwest Missouri State University professor suggests in a column in the Springfield (Mo.) News-Leader the mythical creatures may have been more than just legends:

Today the unicorn is legendary, or mythical. But this was not always so. At one time the unicorn existed--or, at least, was thought to exist.

As described in ancient scientific writings and depicted in painting and tapestry, the unicorn was a beautiful horse-like creature with a single long horn thought to have medicinal properties.

Respected ancient scholars, such as Aristotle and Pliny, mention them existing in their day. But today unicorns have gone the way of fairies, elves, and trolls. Belief in such creatures was abandoned with the 18th century Enlightenment. Oddly enough, however, the unicorn remained a fixture in the Bible until the 19th century.

That sounds very much like the theory put forward by Professor Henry Armitage in my novel, The Mystery of the Haunted Vampire.