Management involves dealing with contradictory demands. For instance, companies have to innovate. Innovation means that past successful behaviours to be discarded, and replaced by others for the company to forge ahead in a new environment. However, companies cannot easily forget the past: their present conditions are shaped by earlier trajectories. How can a company keep its identity, its persona, while changing? This is the essence of paradox. Paradox is central in organization studies, being at the heart of innovation management. Schumpeter\'s idea of \"creative destruction\" is paradoxical in itself. Interestingly, the use of paradox in International Management is relatively limited. This is surprising, having in mind the pervasive nature of dualities (local/global, headquarters/subsidiaries, standardisation/adaptation, core/periphery, centralisation/decentralisation) in the field. It is argued that we might benefit a lot from using paradox lenses in addressing the key international management issues. The paper provides some examples of paradox thinking to improve our understanding about innovation management in multinational companies (MNEs). The focus is put on the paradox of capability as fate versus capability as leverage. This was applied to the rise and fall of a long-lasting MNE: Kodak. It was found that the very capabilities which have fostered Kodak\'s international growth and leadership were the same which led to its fall. Kodak managers did not espouse a paradox approach, aimed at establishing an acceptable trade-off between past capabilities the creation of opportunities for the future. The company fell pray of its past, failing to reinvent itself.