The relationship between solvability of linear diffential-algebraic equations (DAEs) and their transformability into canonical forms has been investigated for more than forty years. After a comparative analysis of numerous DAE frameworks the notions regularity and almost regularity were established only recently. Regular DAEs resulted to be equivalently transformable into so-called standard canonical forms (SCF) with block-structured nilpotent matrix functions featuring certain rank properties. In this paper we prove that for regular DAEs, even a transformation into a strong standard canonical form (SSCF) is possible, i.e. a SCF with a constant nilpotent matrix. We start from block-structured SCF and give a constructive proof.