Peel the banana and wrap it in plastic. Freeze for at least 1-1/2 hours, or until solid.

Place the strawberries in a food processor. Process with on/off pulses until finely chopped; stop several times to scrape down the sides of the container. Then process the mixture for about 1-1/2 minutes, or until very smooth. Scrape down the sides of the container.

With the machine running, add the juice concentrate. Process for 1 minute, or until completely smooth.

Slice the frozen banana. With the machine running, slowly add the slices. Process for at least 1 minute, or until the mixture is completely smooth and creamy. Sweeten to taste with honey; process briefly.

Serve immediately or transfer to a chilled storage container and freeze for 30 minutes.