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Subspace identification methods for multivariable bilinear state-space systems perform computations with data matrices of which the number of rows grow exponentially with the order of the system. Even for relatively low-order systems with only a few inputs and outputs, the amount of memory required to store these data matrices exceeds the limits of what is currently available on the average desktop computer. This severely limits the applicability of the methods. In this paper, we present a kernel method for bilinear subspace identification that performs its computations with kernel matrices which are square matrices with dimensions equal to the number of data samples. For multivariable bilinear systems the kernel matrices have much smaller dimensions than the data matrices used in the original bilinear subspace identification methods. The kernel method significantly reduces the computational complexity of bilinear subspace identification, and allows to use only a small number of data points.