Update 11/07/08: The bank has been closed. Please refer to this post for more details.
Franklin Bank is offering two competitive CD specials: a 4.25% APY 13-month CD and a 4.00% APY 7-month CD. The minimum deposit is $1,000. These CDs don't seem to be listed at the bank's website. A reader emailed me info on these, and I called for more details. According to the CSR, there is no checking requirement. She wasn't sure how long the special would last. It has been around for about 2 weeks.
I was only able to confirm these rates for Franklin's Austin branches. In the Tyler area, Franklin is advertising rates 25 basis points lower (see the online ad). The bank also has branches in several other cities in Texas including Houston, Beaumont, Jacksonville and College Station. If you live near one of these other branches, be sure to call to see what rates are available.
The bank has been FDIC insured since 1987 (FDIC Certificate # 26870). It has a 1-star rating (troubled) at BauerFinancial based on 3/31/08 data. As I recommend with any bank, make sure you stay below the FDIC limits.