We study the restricted one-dimensional central extensions of an arbitrary finite dimensional restricted simple Lie algebra for hURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516304542&_mathId=si1.gif&_user=111111111&_pii=S0024379516304542&_rdoc=1&_issn=00243795&md5=9925cf9a56de4fdf980689b6b6e5d8a0" title="Click to view the MathML source">p≥5. For H2(g)=0, we explicitly describe the cocycles spanning , and in the case H2(g)≠0, we give a procedure to describe a basis for .