>>>>Now why would SSMS create this extra index is beyond me, and I've noticed that it does so. Actually, this is one more on the long list of complaints (if not outright bugs found) that I will add to my list of "what's wrong with SSMS".
>>>
>>>Thank you for the explanation. In truth, in my case, I think I am to blame. That is, the "somehow" is me. After I posted the message I was going through my memory of working on this table. And I believe that the first version of this table the PK field was not a PK but a regular column. That is, I created a table but didn't make any column to be a PK. So I decided to add an index on this column. Later, when I learned a little more, I converted this column to a PK, which created the index PK_TABLE_NAME. But I never deleted the one I created before. So I will delete it now.
>>>Again, thank you.
>>
>>May be true in your case, but I've seen this double indexing too many times. SSMS is still suspect.
>
>I never seen such double indexing by SSMS. Whoever used SSMS incorrectly would be to blame.

I've seen enough bad scripts coming from it, but now with this info from you I think I remember where I saw it. It was probably due to some dbf conversion which first created those indexes and then the PKs were set manually or vice versa, or some such thing. And that may have been done back in the days of SQL 2000 and was never cleaned up, so I still saw it in some of the databases I maintain.