We present a calculation of the one-particle equal time correlation function.(x) for the one-dimensional (1D) Hubbard model in the infinite U limit. We consider the zero temperature spin incoherent regime, which is obtained by first taking the limit U --> infinity and then the limit T --> 0. Using the determinant representation for.(x), we derive analytical expressions for both large and small x at an arbitrary filling factor 0 < rho < 1/ 2. The large x asymptotics of rho(x) is found to be remarkably accurate starting from x sin(2 pi rho) similar to 1. We find that the one-particle momentum distribution function rho(k) is a smooth function of k, and. rho'(k) is peaked at k = 2k(F) in contrast to spin-coherent liquid obeying the Luttinger theorem.