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The methodology to obtain the non-linear roll damping from decay tests is very old. It has been proposed by Froude in the 19th century and used from then on. Behind it there is a quadratic model [θ│θ│] for the damping and a subsequent equivalent linearization. Probably all model basin in the world follows this approach to assess the damping from a decay test. This is well documented and so is the methods to get the p1-p2 coefficients. This is very general in the sense that in principle,it could be applied to any kind of hull. However,it has become clear that for hull with a flat bottom such as a very large crude carrier (VLCC),this approach may lead to confusing results such as negative p2. Faced with this,the work presents a completely new idea. Avoiding the polynomial approximation,the basic attitude is to devise two regions from the decaying test response. The first,called the large amplitude response region yields a larger damping,probably due to the large bilge keel vortices that are attracted to the hull flat bottom. The second is the small amplitude response region where the vortices are not attracted to the bottom but travels approximately 45o sidewise. These observations has led to a new approach called the bi-linear approach as discussed in the work after analyzing several (many) model test results. In fact,a new modified bi-linear approach is ultimately proposed after the understanding of a transition region instead of a transition angle.