The Chinese zodiac animal immediately after the Dragon is the Snake. Dragon is the fifth sign in the traditional twelve-animal cycle, and Snake is the sixth.
The complete sequence is Rat, Ox, Tiger, Rabbit, Dragon, Snake, Horse, Goat, Monkey, Rooster, Dog, and Pig. Because the cycle repeats every twelve years, a Snake year follows every Dragon year, although the exact Lunar New Year date changes from year to year.
The animals are connected to the Earthly Branches of the traditional Chinese calendrical system. Dragon corresponds to chen, while Snake corresponds to si. Zodiac years are also combined with the Five Elements and yin-yang designations, creating a larger 60-year cycle rather than a simple twelve-year repetition of identical labels.
A popular legend explains the order through a race across a river. In that story, the Snake secretly rides on the Horse before jumping ahead near the finish, placing Snake immediately before Horse. The tale is folklore rather than a historical explanation, and zodiac traditions vary across East and Southeast Asia; Vietnam, for instance, uses a Cat where China uses the Rabbit.