A recent problem of interest in Functional Data Analysis (FDA), which generalizes clustering, concerns the discovery of functional motifs in a single curve or in a set comprising multiple curves. Functional motifs are defined as distinctive patterns that are repeated – with a certain amount of noise – within the curve(s) under study. Two methods; namely, probKMA [3] and funBIalign [6], have recently been proposed to tackle this problem. Although they are effective in discovering motifs whose occurrences have similar shape and allow occurrences to be shifted vertically, these methods cannot deal with motifs composed of portions sharing the same shape but having different amplitudes. In this work, we introduce a new definition of motifs based on a multiplicative model that includes this more challenging scenario, and we extend funBIalign to discover amplitude-invariant functional motifs. Performance is assessed through extensive simulations.