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The paper deals with the novel technique of designing complex spreading sequences with only four phases (0.25π, 0.75π, 1.25π, 1.75π). The interesting feature of those new sequences is the fact that not only the complex sequences are orthogonal but the real parts and imaginary parts are independently orthogonal. This can be utilized for spreading of complex constellation signals where the independent spreading using bipolar sequences (real part for in-phase component and imaginary part for quadrature component) can be applied. The paper introduces the theoretical background, and some example constructions of the amicable Hadamard matrices and the corresponding complex spreading sequences. The sequences are later modified using a diagonal method to achieve better correlation properties.