1. Drain artichokes, reserving 1 tablespoon marinade.
2. In a bowl, combine all four types of cheese with the flour. Toss well.
3. In a large saucepan or flameproof fondue pot, combine white wine and reserved 1 tablespoon marinade and bring to a simmer over medium heat.
4. Reduce heat to medium-low. Stir in minced garlic. Add cheese mixture, a handful at a time, stirring constantly in a figure-eight motion with a wooden spoon until cheese is melted.
5. Remove from heat and set up on a fondue stand with a burner if desired. Serve with bread or other dippers.
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