  We revisit the problem of finding the Naimark extension of a probability
operator-valued measure (POVM), i.e. its implementation as a projective
measurement in a larger Hilbert space. In particular, we suggest an iterative
method to build the projective measurement from the sole requirements of
orthogonality and positivity. Our method improves existing ones, as it may be
employed also to extend POVMs containing elements with rank larger than one. It
is also more effective in terms of computational steps.
