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No, the cat is not a Chinese Zodiac Animal.
The animal that represented the Chinese New Year in 1981 was the rooster.
The animal that represented the Chinese New Year in 1940 was the dragon.
The 3rd animal of Chinese Zodiac is the Tiger.
It would be the year of the Horse.
The animal that represented the Chinese New Year for 1919 was the sheep.
The animal that represented the Chinese New Year in 1966 was the horse.
The animal that represented the Chinese New Year in 1971 was the pig.
The animal that represented the Chinese New Year in 1991 was the sheep.
The animal that represented the Chinese New Year in 1962 was the tiger.
The animal that represented the Chinese New Year in 1966 was the horse.
The animal that represented the Chinese New Year in 2003 was the sheep.