Download the updated firmware from the Zoom downloads website. Start up your H4 and look for the firmware version number to appear on the screen. Be sure to download the update that corresponds to the firmware version that is on your H4.
Unzip the downloaded file using WinZip, WinRAR or another file decompression and extraction program. Open the extracted folder and locate the file named "SYSTEM.BIN".
Insert an SD card into your computer's SD card reader, or use a USB cable to connect your computer to your powered-off H4 with the SD card already inside. When the computer recognizes your SD card, drag the SYSTEM.BIN file into the the card's main folder and drop the file there.
Disconnect the H4 from your computer if you connected the two via a USB cable. If you used a separate SD card reader, eject the card and insert it into your H4. Use your AC adapter to power the H4 during the update process. Turn on the H4 while holding down the "Input Menu" button found on the front of the device.
Use the H4's dial control to move the cursor on the display to "OK". Press the dial control button to begin the firmware upgrade process. Wait for the H4's display to read "Complete". Turn off your H4. You can disconnect the AC adapter if you choose.
Turn your Zoom H4 back on. Make sure the firmware version that is displayed upon start up is version 2.40. This is the upgraded version of the H4 firmware. If a different version number is displayed, try the upgrade process again.