We study the problem of a special factorisation of an orthogonal projector P acting in the Hilbert space L2(R) with dimker P < ∞. In particular, we prove that the orthogonal projector P admits a special factorisation in the form P = V V, where V is an isometric upper-triangular operator in the Banach algebra of all linear continuous operators in L2(R). Moreover, we give an explicit formula for the operator V.