The transfer problem is defined by the possibility for a donor country to end up better off after having given away some resources to another country. The simplest version of that problem can be formulated in a two consumer exchange economy with fixed total resources. Existence of a transfer problem at some equilibrium is known to be equivalent to instability in the case of two goods. This characterization is extended to an arbitrary number of goods by showing that a transfer problem exists at a (regular) equilibrium if and only if this equilibrium has an index value equal to -1. Samuelson's conjecture that there is no transfer problem at tatonnement stable equilibria is therefore true for any number of goods.