We consider the φ4 quantum field theory in four dimensions. The Gaussian part of the measure is modified to simulate 4-∊ dimensions where ∊ is small and positive. We give a renormalization group analysis for the infrared behavior of the resulting model. We find that the Gaussian fixed point is unstable but that there is a hyperbolic non-Gaussian fixed point a distance ?(∊) away. In a neighborhood of this fixed point we construct the stable manifold.