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The design of coil for magnetic resonance image (MRI) application is an optimization problem, in which a specified distribution of the magnetic field inside a region of interest is generated by choosing the optimal distribution of current density on a specified non-intersecting design surface. This paper proposes an iterative optimization method for designing MRI coils on a cylindrical surface by using a piecewise discretized scalar stream function as design variable. The surface current density is accurately calculated using piecewise interpolation with smoothness based on the developable property for a cylindrical surface. MRI coils are designed by choosing bi-objective functions and pseudo-Newton sensitivity analysis. The smoothness of the coil are maintained by adjusting the value of derivative degrees of freedom of design variables which are used to interpolate the stream function. Pareto points provide more flexible choices between the two complementary objectives.