So it is NOT this one, from the movie:

THE LAST UNICORN

          When the last eagle flies
          Over the last crumbling mountain
          And the last lion roars
          At the last dusty fountain
          In the shadow of the forest
          Though she may be old and worn
          They will stare unbelieving
          At the Last Unicorn

          When the first breath of winter
          Throught the flowers is icing
          And you look to the north
          And a pale moon is rising
          And it seems like all is dying
          And would leave the world to mourn
          In the distance hear her laughter
          It's the Last Unicorn
          I'm alive... I'm alive

          When the last moon is cast
          Over the last star of morning
          And the future is past
          Without even a last desparate warning
          Then look into the sky where through
          The cloudes a path is formed
          Look and see her how she sparkles
          It's the Last Unicorn
          I'm alive... I'm alive.