In this article, we propose to design a new modular architecture for a self-organizing map (SOM) neural network. The proposed approach, called systolic-SOM (SSOM), is based on the use of a generic model inspired by a systolic movement. This model is formed by two levels of nested parallelism of neurons and connections. Thus, this solution provides a distributed set of independent computations between the processing units called neuroprocessors (NPs) which define the SSOM architecture. The NP modules have an innovative architecture compared to those proposed in the literature. Indeed, each NP performs three different tasks without requiring additional external modules. To validate our approach, we evaluate the performance of several SOM network architectures after their integration on an FPGA support. This architecture has achieved a performance almost twice as fast as that obtained in the recent literature.