  In this paper we reconsider the Cachazo-He-Yuan construction (CHY) of the so
called scattering amplitudes at one-loop, in order to obtain quadratic
propagators. In theories with colour ordering the key ingredient is the
redefinition of the Parke-Taylor factors. After classifying all the possible
one-loop CHY-integrands we conjecture a new one-loop amplitude for the massless
Bi-adjoint $\Phi^3$ theory. The prescription directly reproduces the quadratic
propagators from of the traditional Feynman approach.
