First Hawaiian Inc., the state's second largest bank holding company, today reported that its net income for the three months ending Sept. 30 was down 3.4 percent to $19 million from the year-earlier's $19.7 million due to a one-time, after-tax charge of $2.3 million.

Bancorp Hawaii Inc., the state's largest financial institution, yesterday reported that it's third quarter 1996 net declined 4.8 percent to $31.3 million from the year-earlier quarter's $32.9 million. Bancorp recognized a one-time, after-tax charge of $3 million during the quarter.

For the first nine months this year, First Hawaiian's net was up 4.6 percent to $59.9 million. Bancorp said its year-to-date income increased 10 percent to $98.7 million.

Both banks said the special charges are mandated by a new federal law requiring savings and loan institutions to recapitalize the Savings Association Insurance Fund, which was run down by the mainland S&L crisis of the previous decade.

First Hawaiian's charge reflects its investment in Pioneer Federal Savings Bank and parts of its recently acquired Pacific One Bank. Bancorp owns First Federal Savings and Loan Association.

Minus the charges, First Hawaiian would have earned 69 cents per share for third quarter 1996 while Bancorp would have earned 83 cents per share. Those results were largely in line with Wall Street's expectations.

Share of First Hawaiian rose $0.121/2 to $32.25 on the over-the-counter market at noon today. Bancorp's stock was unchanged at $39.25 at noon on the New York Stock Exchange.