The external plexiform layer is where the interactions between the mitral (excitatory) and granule (inhibitory) cells of the olfactory bulb (OB) take place. Two outstanding features of these interactions are that they are dendrodendritic and that there seem to be none between excitatory cells. The latter are usually credited with the role of forming Hebbian cell assemblies. Hence, it would seem that this structure lacks the necessary ingredients for an associative memory system. In this article we show that in spite of these two properties this system can serve as an associative memory. Our model incorporates the essential anatomical characteristics of the OB. The memories in our system, defined by Hebbian mitral assemblies, are activated via the interactions with the inhibitory granule cells. The nonlinearity is introduced in our model via a sigmoid function that describes neurotransmitter release in reciprocal dendrodendritic synapses. The capacity (maximal number of odors that can be memorized) depends on the sparseness of coding that is being used. For very low memory activities, the capacity grows as a fractional power of the number of neurons. We validate the theoretical results by numerical simulations. An interesting result of our model is that its capacity increases as a function of the ratio of inhibitory to excitatory populations. This may provide an explanation for the dominance of inhibitory cells in the olfactory bulb.