A divisor d of an integer N is called a unitary divisor of N if d and N/d are relatively prime and a biunitary divisor of N if d and N/d have no common unitary divisor except 1. An integer N is called a biunitary triperfect number if the sum σ^**(N) of biunitary divisors of N is equal to 3N. We show that 2160 is the only biunitary triperfect number divisible by 27 = 3³.