This study introduces the Subspace Rotation Algorithm (SRA), an innovative gradientfree method designed to discover the global optimal weight matrix. The SRA consists of two fundamental algorithms: the Left Subspace Rotation Algorithm (LSRA) and the Right Subspace Rotation Algorithm (RSRA). The combination of LSRA and RSRA, in two formats, LSRA-RSRA and RSRA-LSRA, can harness the advantages of both individual algorithms, resulting in enhanced performance. Our observations reveal that shallow and wide Multilayer Perceptrons (MLP), trained using RSRA-LSRA, achieve higher training accuracy compared to the Backpropagation (BP) algorithm. Moreover, when combining SRA with the BP algorithm, a remarkable impact on training MLP models is observed. Our experiments demonstrate that the BP algorithm may become trapped in local optima, while RSRA-LSRA, though capable of escaping local optima, may not fully realize its potential when the number of hidden nodes is limited. The synergy of RSRA-LSRA and the BP algorithm allows for the utilization of the advantages from both approaches, achieving optimal MLP performance with fewer hidden nodes.