Permutation decoding is a technique which involves finding a subset S, called PD-set, of the permutation automorphism group PAut(C) of a code C in order to assist in decoding. A method to obtain s-PD-sets of size s + 1 for partial permutation decoding for the binary linear Hadamard codes H m of length 2 m , for all m ≥ 4 and 1 < s ≤ (2 m − m − 1)/(1 + m) , is described. Moreover, a recursive construction to obtain s-PD-sets of size s + 1 for H m+1 of length 2 m+1 , from a given s-PD-set of the same size for the Hadamard code of half length H m is also established.