  Explicit divergences and counterterms do not appear in the differential
renormalization method, but they are concealed in the neglected surface terms
in the formal partial integration procedure used. A systematic real space
cutoff procedure for massless $\phi^4$ theory is therefore studied in order to
test the method and its compatibility with unitarity. Through 3-loop order, it
is found that cutoff bare amplitudes are equal to the renormalized amplitudes
previously obtained using the formal procedure plus singular terms which can be
consistently cancelled by adding conventional counterterms to the Lagrangian.
Renormalization group functions $\beta (g)$ and $\gamma (g)$ obtained in the
cutoff theory also agree with previous results.
