A new class of composition operators P ϕ : H 2 ( T ) → H 2 ( T ) , with ϕ : T → D ¯ is introduced. Sufficient conditions on ϕ for P ϕ to be bounded and Hilbert-Schmidt are obtained. Properties of P ϕ with ϕ ( e i t ) = a e i t + b e − i t for different values of the parameters a and b have been investigated. This paper concludes with a discussion on the compactness of P ϕ .