Commonwealth Bank of Australia (ASX: CBA) shares are well known for their generosity when it comes to dividend payments.

ASX banks, particularly the big four, have been paying out large and fully franked dividend payments to their investors for decades. At any one time, it's not uncommon to see one or two of the big four trading on fully-franked dividend yields of over 6%.

Owners of CBA shares have been a lucky group of late. They have collectively seen their wealth balloon over the past four or so months. That's been thanks to the CBA share price's rise from around $96 in early November to last month's record high of $121.54 a share.

At present, the CBA share price remains up a healthy 19.44% over the past 12 months.

But this may be ringing alarm bells for some investors. Perhaps those who would like to top up their CBA share piles. Or even those who wish to participate in the bank's regular dividend reinvestment plan (DRP).

As any good dividend investor knows, a company's dividend yield doesn't just depend on the raw dividends per share that are forked out. It is also a function of that company's share price.

Any ASX dividend share's trailing dividend yield is calculated by dividing its raw dividends per share by its share price. So if a company cuts its dividend, the yield is obviously reduced. But it is also reduced if those dividends per share remain the same, but its stock price rises.

To illustrate, last year CBA closed October trading at $96.56 a share. At this stock price, CBA's 2023 total of $4.55 in dividends per share gave the bank a dividend yield of 4.71%. That's decent, if not spectacular, by ASX banking standards.

However, at last month's all-time high CBA share price, those same dividends would give the company a new dividend yield of just 3.74%.

Fortunately for CBA investors, the bank did raise its interim dividend for 2024. Investors enjoyed a rise from $2.10 to $2.15 a share. That would boost CBA's dividend yield at that price to 3.78%.

At the current share price of $119.15 (at the time of writing), our dividend yield is 3.82%.

Now that's nothing for a normal ASX 200 share to be ashamed of. But it's certainly very low by ASX bank standards. To illustrate, CBA's big four sibling ANZ Group Holdings Ltd (ASX: ANZ) shares are presently trading on a yield of 5.95%.

Coles Group Ltd (ASX: COL), Telstra Group Ltd (ASX: TLS) and Transurban Group (ASX: TCL) all currently have higher yields than CBA. Not to mention the other three major banks.

If a shareholder bought CBA shares years ago at a far better price than what they're trading at today, they're probably not too worried. But for any new CBA investors or those that want to add to their positions, this is certainly a consideration to bear in mind.