It is our opinion that over the past 20 years, some atmospheric scientists have used a scientifically incorrect method for finding the contribution of methane to changes in ozone. In any volume element of the atmosphere, the differential equation for ozone D is equal to gross production P minus gross loss L plus transport, which may be written D=P(methane)-L(methane)+P(not methane)-L(not methane)+transport. If both P(not methane) and L(not methane) are effectively zero, then the full differential equation is equal to the differential equation for the effect of methane, D(total)=P(methane)-L(methane)+transport. An approach was introduced around 1980 that has been widely used since then, with the valid assumption that in the lower troposphere the methane smog reactions are the only source of gross ozone production, P(methane). It concluded that the differential rate equation for total ozone change in such regions gives the net ozone change by the methane process (DE method). However, in the lowest troposphere, there are processes not caused by methane that destroy ozone at all altitudes (notably O1D+H2O=2OH), so that L (not methane) is not zero, and thus D=P(methane)-L(methane)-L(not methane)+transport, making the DE method conceptually wrong everywhere. The object of this paper is to solve for how methane changes ozone in the troposphere and stratosphere. Crutzen <1973> gave the first treatment of ozone formation in the global troposphere via methane photooxidation. He considered radical attack on methane to produce CH3 followed by three reaction sequences that go from CH3 to CO2, referred to here as the sequence (SEQ) method. The present study substantially extends Crutzen's sequence method: There are five significant branching points as methane is consumed and 34 sequences (different reaction paths) between CH4 and CO, and more reactions lead to CO2. A detailed derivation is given here, branching ratios are evaluated, and the results are presented as two complicated, closed, algebraic equations, which are valid from the surface up to the middle stratosphere. The SEQ method contains only ozone changes caused by the presence of methane. This method is implemented with output from the 1997 version of the Lawrence Livermore National Laboratory two-dimensional model. Assuming we carried out the SEQ method correctly, we find the DE method to be a fairly good numerical approximation in some areas and a poor numerical approximation in other areas. Averaged over the troposphere, the net effect of the methane smog process is to destroy OH at a rate 32% as fast as it is formed by the nonmethane process, O1D+H2O=2OH. The integral over the global troposphere finds that the net rate of ozone production from methane by the DE is 2.2-fold slower than the SEQ method. ¿ 1998 American Geophysical Union