Abstract: A new triangle summation operator, T_n(f;x), is constructed via linearly combini ng several known operators. It is proved that this operator converges t o arbitrary continuous function f(x) with period 2π on the whole axis. If f(x)∈C^j_2π(0≤j≤7), the best convergence order of the op erator is obtained. Finally, it is proved that the highest convergence order of the operator does not exceed 1/n⁸. The new operator constructed in th is paper is superior to other operators in convergency.

Key words: triangle summation operator, uniform convergence, b est approximation order