Quantum combinatorial designs are gaining popularity in quantum information theory. Quantum Latin squares can be used to construct mutually unbiased maximally entangled bases and unitary error bases. Here we present a general method for constructing quantum Latin arrangements from irredundant orthogonal arrays. As an application of the method, many new quantum Latin arrangements are obtained. We also find a sufficient condition such that the improved quantum orthogonal arrays [10] are equivalent to quantum Latin arrangements. We further prove that an improved quantum orthogonal array can produce a quantum uniform state.