diff --git a/API_reference.py b/API_reference.py
index 000844e..2349b25 100644
--- a/API_reference.py
+++ b/API_reference.py
@@ -66,7 +66,7 @@ eigenvector = guan.calculate_eigenvector(hamiltonian)
 
 # find vector with the same gauge    # Source code: https://py.guanjihuan.com/find_vector_with_the_same_gauge
 vector_target = guan.find_vector_with_the_same_gauge_with_binary_search(vector_target, vector_ref, show_error=1, show_times=0, show_phase=0, n_test=10001, precision=1e-6)
-vector = guan.find_vector_with_fixed_gauge_by_making_one_component_real(vector, precision=0.005)
+vector = guan.find_vector_with_fixed_gauge_by_making_one_component_real(vector, precision=0.005, index=None)
 
 # calculate Green functions    # Source code: https://py.guanjihuan.com/calculate_green_functions
 green = guan.green_function(fermi_energy, hamiltonian, broadening, self_energy=0)
diff --git a/PyPI/setup.cfg b/PyPI/setup.cfg
index 025356a..7d90350 100644
--- a/PyPI/setup.cfg
+++ b/PyPI/setup.cfg
@@ -1,7 +1,7 @@
 [metadata]
 # replace with your username:
 name = guan
-version = 0.0.15
+version = 0.0.16
 author = guanjihuan
 author_email = guanjihuan@163.com
 description = An open source python package
diff --git a/PyPI/src/guan/find_vector_with_the_same_gauge.py b/PyPI/src/guan/find_vector_with_the_same_gauge.py
index ed81530..7513211 100644
--- a/PyPI/src/guan/find_vector_with_the_same_gauge.py
+++ b/PyPI/src/guan/find_vector_with_the_same_gauge.py
@@ -42,8 +42,9 @@ def find_vector_with_the_same_gauge_with_binary_search(vector_target, vector_ref
         print('Phase=', phase)   
     return vector_target
 
-def find_vector_with_fixed_gauge_by_making_one_component_real(vector, precision=0.005):
-    index = np.argmax(np.abs(vector))
+def find_vector_with_fixed_gauge_by_making_one_component_real(vector, precision=0.005, index=None):
+    if index == None:
+        index = np.argmax(np.abs(vector))
     sign_pre = np.sign(np.imag(vector[index]))
     for phase in np.arange(0, 2*pi, precision):
         sign =  np.sign(np.imag(vector[index]*cmath.exp(1j*phase)))