A closed-form kinetic energy operator (KEO) for tetra-atomic planar molecules in Eckart frame has been expressed explicitly in terms of the internal coordinates with a parameter theta(1e) which labels a specific Eckart frame. This KEO has zero Coriolis coupling at equilibrium and an expression for the best theta(1e) has been given that makes zero centrifugal coupling. A method treating the singularities of this KEO has been shown and all matrix elements are finite in the basis presented in this paper. (C) 2003 American Institute of Physics.