If you were on the hunt for bank stocks with the best potential for dividend increases over the years to come, then there are four big banks in particular that you need to check out: The Bank of New York Mellon (NYSE:BK), Goldman Sachs (NYSE:GS), Bank of America (NYSE:BAC), and Citigroup (NYSE:C). These four banks currently have the lowest dividend yields among the nation's biggest banks.

The reasons these bank stocks have such low yields vary. Bank of America, Citigroup, and The Bank of New York Mellon all had to cut their dividends significantly during the financial crisis. Goldman Sachs, meanwhile, has only recently started to pay a dividend, meaning that there's still considerable time for its payout to season.

But regardless of the explanation, given that these bank stocks compete for shareholders' capital against higher-yielding banks, it seems safe to assume that they'll make an added effort over the years ahead to bring their own quarterly payouts up to the levels of their higher-yielding peers.

To see exactly where these four banks rank in terms of dividend payout, scroll through the brief slideshow below.

Source: Dividend yield data for The Bank of New York Mellon, Goldman Sachs, Bank of America, and Citigroup was sourced from Yahoo! Finance.