A directed search for extraterrestrial intelligence (SETI) has been ca
rried out using the IRAM 30m telescope. Following a suggestion by Kard
ashev (1979), the search was conducted at the spin-flip line of the li
ghtest atom, namely positronium, at 203 GHz. Most of the 17 targets ar
e mature stars with excess infrared radiation, which might be the wast
e heat of a power-rich technological civilisation. The rest frame of t
he cosmic background radiation was chosen as the velocity frame. The s
pectral resolution used was 9.7 kHz. From the noise level, which was d
etermined by the limited telescope time and weather conditions, the up
per limit for the power of artificial omnidirectional transmitters at
the positronium line frequency is of order 10(15) W. The relevance of
this non-detection is discussed.