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We analyze "almost Hadamard matrices"- orthogonal matrices of a given order N with modulus of all elements distributed as uniform as possible.Formally an Almost Hadamard matrix is an orthogonal matrix,for which the 1-norm on O(N) achieves a local maximum.Our study includes a discussion the two-entry case closely linked to balanced incomplete block designs (BIBD).A another generalization of real Hadamard matrices is obtained if one considers complex unitary matrices with entries of the same modulus.A brief review of problems related to complex Hadamard matrices and Mutually Unbiased Bases (MUB) is also presented.