When using static member variables they are not instantiated every time that the an instance of the surrounding class is instantiated, they are only instantiated once, the first time that the class is loaded.
In your case, assuming that your Map can never change, then it is best to mark it as final, to ensure that it can never change, and wrap it in an unmodifiableMap to ensure that it cannot be modified.
For example:
private static final HashMap<String, String> map;
static {
HashMap<String, String> tmpMap = new HashMap<String, String>()
tmpMap.put("A", "aba");
map = Collections.unmodifiableMap(tmpMap);
}