My best guess is metal spring clips holding it in place internally.

This is the most terrifying option because the only way to find out is to give it a good yank. Well, a careful yank. Maybe trying to yank it to one side.

Here is a link that might be useful: How to open twist off the cover of some really stupid awkward flush mounted ceiling light

This post was edited by robotropolis on Thu, Jan 15, 15 at 13:02

Things like that were designed to make us feel stupid! Do you hear it laughing at you every time you approach with a stepstool, Suero?

Does it screw off? Cool light - its amazing to me how weirdly some lights are built. When you do figure it out use LED's - good for 25 years ;0

I've tried to unscrew the ring, but all I could do is tilt the globe a bit (and pinch my finger when the globe snapped back). The light is more than 30 years old, so I'm sure that I've changed a bulb sometime in the past, but it has been so many years that I can't remember if I ever changed the bulb and if so, what I did.

To see if it has clips holding it up, carefully slide a butter knife between the globe and the metal. Try prying the globe away from the metal part. If it comes loose you may need to do that all around the globe. I have one similar that is held on by 3 clips.

I got the definitive answer. It took three people. One to turn off the circuit breaker. One to unscrew the light fixture (while the other one held the bottom to make sure it didn't fall and break in the process), and the terrific man in the lighting fixture store who took the globe off its base so that new light bulbs could be screwed in.
Now all we have to do is reinstall the light fixture. And hope these bulbs last a long, long time.

No pictures?

Not enough hands to take a picture of us unscrewing the fixture. Oh, the inside? Well, there's spring that holds the bulb in place, and you have to do a push and slide to get the bulb off the stem.

So what are u gonna do when the next light goes out. Lol. Talk about a pain. Shoulda got a new light fixture while you had it taken down.

Once we got the light fixture down, I could see the manufacturer's name Lightcraft of California. I googled the name and found the patent application for the mechanism that attaches the globe to the stem. Now that I have that information, along with an exploded drawing of the internal mechanism, I'll be able to change the light bulbs in the future.
As for the fixture itself, I found it for sale on several sites, including 1st dibs, where it had already been sold. Apparently, this 1960's fixture is very popular. Maybe because people like the look, but have not yet tried to change a burnt out bulb in ths fixture.