Predicting the effective viscosity of a foam as a function of its bubble size, liquid fraction and chemical composition is still an open question. The confinement of the liquid phase between the bubbles is expected to strongly enhance the local deformation rates. However, these local deformations are induced by interfacial stresses, which are limited by the surface tension accessible range: above a critical bubble size and/or shear rate, it is impossible to shear the whole film separating the bubbles. In this paper, we investigate this large bubble regime by imposing a simple shear to a minimal foam made of five interconnected films. We present a new local deformation pattern, with a relaxation process lasting long after the motor stops, that we characterize for a large range of shear rate and for different foaming solutions. A direct evidence of the absence of shear during the relaxation has been obtained for one solution. At 10 s−1, this original large bubble regime should be relevant for foams with bubbles larger than 300 microns.