  We study three same spin state fermions of mass M interacting with a
distinguishable particle of mass m in the unitary limit where the interaction
has a zero range and an infinite s-wave scattering length. We predict an
interval of mass ratio 13.384 < M/m < 13.607 where there exists a purely
four-body Efimov effect, leading to the occurrence of weakly bound tetramers
without Efimov trimers.
