on an old article I came to know about this Howland Circuit. It was mentioning improved howland vs. original howland circuit. Is the resistor R4 is the difference between them? Is the function of this R4 stays only for trimming the precision?
See e.g. TI application note AN-1515. Trimming (of resistor mismatch) is possible and necessary also in the basic howland circuit. R4 is mainly an option to adjust the circuit behavior regarding in- to output voltage range.