A Haar shift operator has been introduced in \cite{pet} as a new tool to prove
results about Calder\'on-Zygmund operators. It is constructed using Haar basis,
and an appropriate average of it recovers the Hilbert transform. Other
Calder\'on-Zygmund operators can also be studied in this way. The Haar shift
operator has become a powerful tool. We look at this operator in the context of
a more general wavelet basis, and prove a convergence theorem.