  Let R be a semi-local regular ring containing an infinite perfect field, and
let K be the field of fractions of R. Let H be a simple algebraic group of type
F_4 over R such that H_K is the automorphism group of a 27-dimensional Jordan
algebra which is a first Tits construction. If char K is not 2, this means
precisely that the f_3 invariant of H_K is trivial. We prove that if an
H-torsor is rationally trivial, then it is trivial over R. This result is a
particular case of the Grothendieck-Serre conjecture. It continues the recent
series of papers by I. Panin, N.Vavilov and the authors, and complements the
result of V. Chernousov on the Grothendieck-Serre conjecture for groups of type
F_4 with trivial g_3 invariant.
