Two observers are assumed to move along the $X$ axis and to measure the components of the electric intensity $E(E_1,E_2,E_3)$ and magnetic intensity $H(H_1,H_2,H_3)$ of a plane electromagnetic wave propagated at an arbitrary angle to the $X$ axis. According to the theory of relativity, the two observers will find the same values of the components $E_1$ and $H_1$ along the $X$ axis. The components $E_2,E_3,H_2,H_3$, along the $Y$ and $Z$ axes, are replotted in a novel manner in the so-called computing plane which consists of two sets of oblique co-ordinates. The angle comprised by each set is uniquely determined by the relative velocity of the two observers. In the computing plane a transformation point $M$ is located such that its abscissa and ordinate with respect to one set of oblique axes gives the components $E_2$ and $H_3$ of the wave intensities as measured by one of the observers, while its co-ordinates with respect to the other set of axes gives the values of the same components as measured by the other observer. Another transformation point $N$ gives the components $E_{15}$ and $H_2$ for the two observers. It is shown that the loci of $M$ and $N$ are ellipses. The results obtained are shown to check with the well-known equations of the theory of relativity. The location of the points $M$ and $N$ is shown in two simple special cases, and instructions are given for locating them in the general case.

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