We present a method which provides some information on the possible binary nature of an apparently single star .
The method compares the instantaneously measured HIPPARCOS proper motion with the long-term averaged , ground-based proper motion or with the proper motion derived from old ground-based positions and the HIPPARCOS position .
Good sources for such ground-based data are the FK5 and the GC .

If the proper-motion difference \Delta \mu is statistically significant with respect to its measuring error , the object is very probably a double star .
We call then the object a ’ delta-mu binary ’ .
If the proper-motion difference is insignificant and if no other information on a binary nature of the object is available , we call such a star a ’ single-star candidate ’ .

We propose a quantitative test for the significance of the observed proper-motion difference .
The sensitivity of our method is high : For nearby stars at a distance of 10 pc , the measuring accuracy of the proper-motion difference , expressed as a velocity , is of the order of 50 m/s ( basic FK5 stars ) or 80 m/s ( GC stars ) .
At 100 pc , the mean error of the two-dimensional difference is still 0.5 km/s or 0.8 km/s .

For the FK5 stars , we provide indications on the probable period of the \Delta \mu binaries .
If we adopt an orbital period and a mass-luminosity relation , we can use the observed velocity difference to estimate the separation and the magnitude difference between the two components of the binary .

The present paper concentrates mainly on the basic principles of the method , but it provides also a few examples of delta-mu binaries and of single-star candidates for illustration : \gamma UMa , \varepsilon Eri , \iota Vir , 47 UMa , \delta Pav .