Multiquadric collocation method is highly efficient for solving partial differential equations due to its exponential error convergence rate. More amazingly, there are two ways to reduce the error: the traditional way of refining the grid, and the unexpected way of simply increasing the value of shape constant $c$ contained in the multiquadric basis function, $sqrt{r^2 + c^2}$. The latter is accomplished without increasing computational cost. It has been speculated that in a numerical solution without roundoff error, infinite accuracy can be achieved by letting $c ightarrow infty$. The ability to obtain infinitely accurate solution is limited only by the roundoff error induced instability of matrix solution with large condition number. Using the arbitrary precision computation capability of {it Mathematica}, this paper tests the above conjecture. A sharper error estimate than previously obtained is presented in this paper. A formula for a finite, optimal $c$ value that minimizes the solution error for a given grid size is obtained. Using residual errors, constants in error estimate and optimal $c$ formula can be obtained. These results are supported by numerical examples.