Context :

Aims : Using an accurate Gaia TGAS 25 pc sample , nearly complete for GK stars , and selecting common proper motion ( CPM ) candidates from UCAC5 , we search for new white dwarf ( WD ) companions around nearby stars with relatively small proper motions .

Methods : For investigating known CPM systems in TGAS and for selecting CPM candidates in TGAS + UCAC5 , we took into account the expected effect of orbital motion on the proper motion as well as the proper motion catalogue errors .
Colour-magnitude diagrams ( CMDs ) M _ { J } / J - K _ { s } and M _ { G } / G - J were used to verify CPM candidates from UCAC5 .
Assuming their common distance with a given TGAS star , we searched for candidates that occupied similar regions in the CMDs as the few known nearby WDs ( 4 in TGAS ) and WD companions ( 3 in TGAS + UCAC5 ) .
CPM candidates with colours and absolute magnitudes corresponding neither to the main sequence nor to the WD sequence were considered as doubtful or subdwarf candidates .

Results : With a minimum proper motion of 60 mas/yr , we selected three WD companion candidates , two of which are also confirmed by their significant parallaxes measured in URAT data , whereas the third may also be a chance alignment of a distant halo star with a nearby TGAS star .
( angular separation of about 465 arcsec ) .
One additional nearby WD candidate was found from its URAT parallax and GJK _ { s } photometry .
With HD 166435 B orbiting a well-known G1 star at \approx 24.6 pc with a projected physical separation of \approx 700 AU , we discovered one of the hottest WDs , classified by us as DA2.0 \pm 0.2 , in the solar neighbourhood .
We also found TYC 3980-1081-1 B , a strong cool WD companion candidate around a recently identified new solar neighbour with a TGAS parallax corresponding to a distance of \approx 8.3 pc and our photometric classification as \approx M2 dwarf .
This raises the question whether previous assumptions on the completeness of the WD sample to a distance of 13 pc were correct .

Conclusions :