  We investigate whether the seven-loop beta function of the $\lambda \phi^4_4$
theory exhibits evidence for an ultraviolet zero. In addition to a direct
analysis of the beta function, we calculate and study Pad\'e approximants and
discuss effects of scheme transformations on the results. Confirming and
extending our earlier studies of the five-loop and six-loop beta functions, we
find that in the range of $\lambda$ where the perturbative calculation of the
seven-loop beta function is reliable, the theory does not exhibit evidence for
an ultraviolet zero.
