The integrodifferential equation describing the linear tearing instability in the bi‐Maxwellian neutral sheet is solved without approximating the particle orbits or the eigenfunction &psgr;. Results of this calculation are presented. Comparison between the exact solution and the three‐region approximation [Phys. Fluids27, 1198 (1984)] motivates the piecewise‐straight‐line approximation, a simplification that allows faster solution of the integrodifferential equation, yet retains the important features of the exact solution.