The Japanese believe in the future of California’s housing market.

Mitsubishi UFJ Financial Group increased its bid to gain full control of UnionBanCal (UB) to $3.5 billion, an increase of 17%. UnionBanCal has about 300 branches in California.

In general, Japanese banks have avoided most of the subprime mortgage problems, but, facing slow growth at home, are now looking to the United States for growth. Mitsubishi is seeking the 35% of the California lender it doesn’t already own.

Mitsubishi raised its offer to $73.50 a share after UnionbanCal’s directors rejected last week’s offer of $63 a share. Mitsubishi UFJ Financial Group’s latest bid represents a 12% premium to UnionBanCal’s Friday closing price of $65.49 and is 27% higher than Mitsubishi’s initial bid of $58 made in April.

Mitsubishi says it wants to diversify beyond the souring Japanese market and boost its presence in the US, despite the subprime mess and a souring economy. Clearly, Mitsubishi is taking the long view.

Overall, the US banking system appears to be in less danger now than it was in the late 1980s and early 1990s, when about 1,000 federally insured institutions failed in the savings-and-loan debacle.

The FDIC insures deposits at about 8,500 banks and thrifts. Coverage is limited to $100,000 per institution and $250,000 on some retirement accounts.

The Certificate of Deposit Account Registry Service -- or CDARS, pronounced “cedars” like the trees -- enables borrowers to place CDs at several banks to keep each below the $100,000 limit for full FDIC coverage.