This authors develop a novel technique for blind source separation (BSS) of nonlinearly mixed signals. A new type of nonlinear mixture is derived where a linear mixing matrix is slotted between two layers of multiple mutually inverse nonlinearities. The paper discusses the separability of this new mixing model within the BSS context. This model further culminates to a framework where the separation solution integrates the theory of series reversion with the Weierstrass neural network and the hidden neurons are spanned by a set of mutually inversed activation functions. Simulations have been undertaken to support the theory of the developed scheme and the results indicate promising performance. The proposed method outperforms other tested algorithms in recovering both synthetic and the real-life recorded signals. The method of selecting the optimum order of the Weierstrass series has also been derived and implemented to balance the computational complexity and the accuracy of signal separation.