This was a run-down but charming apartment house reminiscent of the architecture of Ödön Lechner; it could have been designed by him, but there was no way of telling. If this isn't his creation, then it surely is one of his students.
The famous Hungarian architect Ödön Lechner employed the Secession style, a variation of Art Nouveau that incorporates elements of Hungarian folk art and which became the Hungarian national style. Masterpieces by Lechner include the Geology Institute http://www.pbase.com/helenpb/image/130482111, the Postal Savings Bank http://www.pbase.com/helenpb/image/130678536, Szent Laszlo Church http://www.pbase.com/helenpb/image/130490945, a villa http://www.pbase.com/helenpb/image/130489212, Kecskemet City Hall http://www.pbase.com/helenpb/image/130648750 and the Applied Arts Museum http://www.pbase.com/image/128557313.
Information on Lechner is here: http://en.wikipedia.org/wiki/Ödön_Lechner