In a word, no. The 802.11g standard was designed to be backward compatible with 802.11b, and to make that crystal clear, many vendors prefer to market their 802.11g products as 802.11g/b. Unfortunately, 802.11b was not designed with 802.11g in mind, so although you can use 802.11b gear to connect to 802.11g networks, you're stuck with 802.11b speeds, and no firmware update to date will convert an 802.11b device into an 802.11g device.

The easiest way for you to move to 802.11g with your current setup is to add an 802.11g PC Card adapter to your notebook. If your D-Link router is equipped with an Atheros chipset and supports Super-G mode, as the DI-624 does, you can add a corresponding Super-G adapter, such as the DWL-G650, and get significantly faster speeds than you would get with standard 802.11g.