A new filter topology for a second-order absorptive bandstop filter with Butterworth response is presented in this paper. Closed-form design equations for having a Butterworth transmission response and no reflection at all frequencies are also provided. Hence, an absorptive bandstop filter can be designed such that its transmission response is identical to the one of a conventional reflective filter. For verifying the presented filter topology and design formulas, an absorptive bandstop filter with 10% fractional bandwidth centered at 190 MHz has been designed, fabricated, and measured. The measurement shows that the fabricated filter has the return loss larger than 15 dB in the stopband and the Butterworth response in the power transmission.