Chelsea were fined 65,000 pounds and West Brom 35,000 pounds.
The charge referred to the heated aftermath of West Brom's Claudio Yacob escaping a second booking after fouling Diego Costa in the second half of the 2-2 draw at Stamford Bridge.
The game was a fractious affair with firebrand Chelsea striker Costa involved in several spats, including an incident with most of the West Brom team after the final whistle.
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Chelsea were also fined for misconduct in November following their bad-tempered Premier League clash with West Ham United.
(Reporting by Justin Palmer, editing by Pritha Sarkar)
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