diff --git a/src/modules/common/moduleRandom.f90 b/src/modules/common/moduleRandom.f90
index ae5c548..7d9cec6 100644
--- a/src/modules/common/moduleRandom.f90
+++ b/src/modules/common/moduleRandom.f90
@@ -66,6 +66,23 @@ MODULE moduleRandom
 
     END FUNCTION randomMaxwellian
 
+    !Returns a random number in a Maxwellian distribution of mean 0 and width 1
+    FUNCTION randomHalfMaxwellian() RESULT(rnd)
+      IMPLICIT NONE
+
+      REAL(8):: rnd
+      REAL(8):: x
+
+      rnd = 0.D0
+      x = 0.D0
+      DO WHILE (x == 0.D0)
+        CALL RANDOM_NUMBER(x)
+      END DO
+
+      rnd = DSQRT(-DLOG(x))
+
+    END FUNCTION randomHalfMaxwellian
+
     !Returns a random number weighted with the cumWeight array
     FUNCTION randomWeighted(cumWeight, sumWeight) RESULT(rnd)
       IMPLICIT NONE
diff --git a/src/modules/moduleInject.f90 b/src/modules/moduleInject.f90
index b4e0ed2..b6fc64b 100644
--- a/src/modules/moduleInject.f90
+++ b/src/modules/moduleInject.f90
@@ -298,10 +298,7 @@ MODULE moduleInject
       REAL(8):: v
       v = 0.D0
 
-      DO WHILE (v <= 0.D0)
-        v = self%vTh*randomMaxwellian()
-
-      END DO
+      v = self%vTh*randomHalfMaxwellian()
 
     END FUNCTION randomVelHalfMaxwellian